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Studying the Transverse Spin Structure of the Proton at

Studying the Transverse Spin Structure of the Proton at. Columbia University. Christine Aidala. Indiana University. October 3, 2005. Experimental Data on Proton Structure. polarized. g 1. Q 2 (GeV 2 ). unpolarized. F 2. Q 2 (GeV 2 ). Spin Structure of the Proton: Status.

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Studying the Transverse Spin Structure of the Proton at

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  1. Studying the Transverse Spin Structure of the Proton at Columbia University Christine Aidala Indiana University October 3, 2005

  2. Experimental Data on Proton Structure polarized g1 Q2 (GeV2) unpolarized F2 Q2 (GeV2) C. Aidala, Indiana U., Oct. 3, 2005

  3. Spin Structure of the Proton: Status Parton Distributions: (well known) (moderately well known) (unknown) (moderately well known) (basically unknown) C. Aidala, Indiana U., Oct. 3, 2005

  4. Polarized Quark and Gluon Helicity Distributions EMC, SMC at CERN E142 to E155 at SLAC HERMES at DESY Quark spin contribution to the proton spin: “Spin Crisis” The rest from gluons and orbital angular momentum. Measurement of gluon and sea distributions a major focus of RHIC spin program. up quarks gluon sea quarks down quarks But what about the transverse spin structure of the proton? C. Aidala, Indiana U., Oct. 3, 2005

  5. Quark Distributions and Helicity Elastic proton-quark scattering (related to inelastic scattering through optical theorem) Helicity basis not “natural” here. Helicity flip distribution also called the “transversity” distribution. Corresponds to the difference in probability of scattering off of a transversely polarized quark within a transversely polarized proton with the quark spin parallel vs. antiparallel to the proton’s. Three independent pdf’s corresponding to following helicity states: Take linear combinations to form: Helicity average Helicity difference Helicity flip C. Aidala, Indiana U., Oct. 3, 2005

  6. Longitudinal vs. Transverse Spin Structure • Transverse spin structure of the proton cannot be deduced from longitudinal (helicity) structure • Spatial rotations and Lorentz boosts don’t commute • Relationship between longitudinal and transverse structure provides information on the relativistic nature of partons in the proton • Transverse structure linked to intrinsic parton kT and orbital angular momentum C. Aidala, Indiana U., Oct. 3, 2005

  7. q(x1) Hard Scattering Process X g(x2) Universality Hard Scattering in (Unpolarized) p+p:Factorization and Universality • “Hard” probes have predictable rates given: • Parton distribution functions (need experimental input) • pQCD hard scattering rates (calculable in pQCD) • Fragmentation functions (need experimental input) C. Aidala, Indiana U., Oct. 3, 2005

  8. |h| < 0.35 hep-ex/0507073 Accepted to PRL Mid-rapidity Cross Section Measurements PRL 91, 241803 (2003) • NLO pQCD consistent with data within theoretical uncertainties. • pdf’s: CTEQ5M • Fragmentation functions: • Kniehl-Kramer-Potter (KKP) • Kretzer • Spectrum constrains D(gluon p) fragmentation function • Important confirmation of theoretical foundation for spin program • Factorization applicable, with small scale dependence p0 |h| < 0.35 9.6% normalization error not shown C. Aidala, Indiana U., Oct. 3, 2005

  9. kT-dependent pdf’s and FF’s • Collinear factorization—assumes partons have momentum collinear to parent hadron • pdf’s and FF’s integrated in kT • Allowing kT dependence to remain yields several possible new pdf’s and FF’s • kT-dependent QCD currently a vibrant area of theoretical investigation • What are the effects of soft scales in hard processes? • Transverse spin observables (at high energy scales) one of few experimental probes sensitive to kT dependence in pQCD C. Aidala, Indiana U., Oct. 3, 2005

  10. RHIC Physics Broadest possible study of QCD in A+A, p+A, p+p collisions • Heavy ion physics • Investigate nuclear matter under extreme conditions • Examine systematic variations with species and energy • Nucleon structure in a nuclear environment • Nuclear dependence of pdf’s • Saturation physics • Proton spin structure • In particular, contributions from • Gluon polarization (Dg) • Sea-quark polarization • Advantages of a polarized hadron collider • High energy  factorization, new probes (W’s) • Polarized hadrons  gq, gg collisions C. Aidala, Indiana U., Oct. 3, 2005

  11. The Relativistic Heavy Ion Collider • Heavy ions, polarized protons • Most versatile collider in the world! Nearly any species can be collided with any other. • asymmetric species possible due to independent rings with separate steering magnets C. Aidala, Indiana U., Oct. 3, 2005

  12. 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, Indiana U., Oct. 3, 2005

  13. RHIC PHENIX STAR LINAC AGS Siberian Snakes To Maintain Polarization Effect of depolarizing resonances averaged out by rotating spin by 180 degrees on each turn • 4 helical dipoles in each snake • 2 snakes in each ring • - axes orthogonal to each other C. Aidala, Indiana U., Oct. 3, 2005

  14. 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 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, Indiana U., Oct. 3, 2005

  15. 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 2005 data • Both use asymmetries in processes that are already understood to determine the beam polarization C. Aidala, Indiana U., Oct. 3, 2005

  16. RHIC’s Experiments Transverse spin only (No rotators) Longitudinal or transverse spin Longitudinal or transverse spin C. Aidala, Indiana U., Oct. 3, 2005

  17. The PHENIX Collaboration 13 Countries; 62 Institutions; 550 Participants as of 3/05 C. Aidala, Indiana U., Oct. 3, 2005

  18. The PHENIX Detector • Philosophy: • High rate capability & granularity • Good mass resolution and particle ID • Sacrifice acceptance • 2 central spectrometers • - Track charged particles and detect electromagnetic processes • 2 forward spectrometers • - Identify and track muons • 2 global detectors • - Determine when there’s a collision C. Aidala, Indiana U., Oct. 3, 2005

  19. 2001-02 Au+Au 2002-03 d+Au Au+Au and d+Au Collisions in the PHENIX Central Arms p+p multiplicities a tiny fraction of Au+Au! C. Aidala, Indiana U., Oct. 3, 2005

  20. 2001-2 Transversely polarized p+p collisions Average polarization of ~15% Integrated luminosity 150 nb-1 Figure of merit (P2L) 3.38 nb-1 2003 Longitudinally polarized p+p collisions achieved Average polarization of ~27% Integrated luminosity 220 nb-1 Figure of merit (P4L) 1.17 nb-1 2004 5 weeks commissioning, 4 days data-taking Average polarization ~40% Integrated luminosity 75 nb-1 Figure of merit (P4L) 1.92 nb-1 2005 Average polarization ~48% Integrated longitudinal lumi 3.59 pb-1 Figure of merit (P4L) ~1.9 pb-1 Integ. transverse lumi 0.163 pb-1 Figure of merit (P2L) 0.038 pb-1 Spin Running at PHENIX So Far C. Aidala, Indiana U., Oct. 3, 2005

  21. Production Heavy Flavors Prompt Photon Proton Spin Structure at PHENIX C. Aidala, Indiana U., Oct. 3, 2005

  22. left right Transverse Single-Spin Asymmetries AN E704 at Fermilab at s=19.4 GeV, pT=0.5-2.0 GeV/c: • Large left-right asymmetries (~20-40%) seen in particle production with a vertically polarized beam or target at AGS and Fermilab experiments • Origin remains unclear even now, but several different mechanisms proposed C. Aidala, Indiana U., Oct. 3, 2005

  23. Transverse Single-Spin Asymmetries (cont.) • General form for transverse SSA’s: • Collinear momenta would produce no effect • Thus importance of kT • Spin could be of initial proton or struck quark • Possible momenta include initial proton momentum, final-state particle or jet momentum, kT of parton within proton, kT of final-state particle with respect to jet axis • Lots of combinations possible! C. Aidala, Indiana U., Oct. 3, 2005

  24. Sivers Effect • Spin-dependent intrinsic transverse momentum of the partons • Sivers (kT-dependent) pdf • Related to orbital angular momentum • “Fan” interpretation of Dennis Sivers—think of a ball being dropped onto a spinning fan from above • But need some kind of shadowing or opacity to make scattering off the “front” of the proton more likely C. Aidala, Indiana U., Oct. 3, 2005

  25. Collins effect (fragmentation) L=1 dq(x) Collins Effect • Fragmentation of a transversely polarized quark into a spinless hadron has an azimuthal dependence • Collins (kT-dependent) FF • Requires non-zero transversity Collins animation: collins_animation.htm C. Aidala, Indiana U., Oct. 3, 2005

  26. Spin-dependent quantum correlations between quarks and gluons in the hadron Possible in either the initial-state nucleon or fragmentation to the final-state hadron Notable work by Qiu and Sterman, Koike Debate within theoretical community about relation to other mechanisms Initial-state correlations equivalent to phenomenological models of Sivers effect? Quark-Gluon Correlations C. Aidala, Indiana U., Oct. 3, 2005

  27. Large SSA’s Persist at RHIC Energies: STAR Forward p0 Results • Contributions from Sivers effect, Collins effect, and initial- or final-state quark-gluon correlations all possible • Theoretical curves scaled from fits to E704 data at 19.4 GeV • Agree reasonably with data • Implications not yet clear—still too many possibilities and unknowns in transverse spin structure! <> = 3.7 PRL 92 (2004) 171801 C. Aidala, Indiana U., Oct. 3, 2005

  28. AN Raw asym Preliminary Preliminary Raw asym xF < 0 xF*100 protons pT (GeV/c) Transverse Single-Spin Asymmetries for p+, p-, and Proton Production at BRAHMS Note STAR also measured zero asymmetry for p0 production at negative xF C. Aidala, Indiana U., Oct. 3, 2005

  29. AN = 0.110±0.015 preliminary Forward Neutron Asymmetry at RHIC • Large and negative (-11%) • Observed at 200 and 410 GeV • ~Zero for backward neutrons • Why large asymmetry for forward neutrons but not forward protons?? (But admittedly not same kinematics) C. Aidala, Indiana U., Oct. 3, 2005

  30. Radial polarization f Neutron Asymmetry vs. f (Raw Asymmetry) / (beam pol.) Vertical polarization f C. Aidala, Indiana U., Oct. 3, 2005

  31. Other Recent Measurements in Transverse Spin Physics • HERMES’s non-zero measurements of both Sivers and Collins moments in DIS • COMPASS’s zero measurements of Sivers and Collins in DIS • Understood to be due to cancellations in deuteron target • BELLE measurement of the Collins FF for pions • Essential to understand the Collins mechanism as a potential contributor to the observed asymmetries • Collins effect requires convolution of transversity distribution function and Collins FF, and previously both were unknown! C. Aidala, Indiana U., Oct. 3, 2005

  32. It’s (Still) a Jungle Out There • Despite lots of work on transverse spin structure in recent years, no single, clear formalism in which to interpret the observed asymmetries has emerged yet • Additional measurements covering a wide kinematic range will be important in disentangling the various possible contributions to the observed asymmetries C. Aidala, Indiana U., Oct. 3, 2005

  33. AN of Mid-rapidity Neutral Pions and Charged Hadrons at PHENIX • xF ~ 0.0 • Compare to STAR xF > 0.2, BRAHMS xF > 0.15 • First mid-rapidity results from RHIC • 2001-02 data • p0 : 1 < pT < 5 GeV/c • h+, h- : 0.5 < pT < 5 GeV/c C. Aidala, Indiana U., Oct. 3, 2005

  34. Measuring AN at PHENIX Consider polarization and spin states of one beam, average over spin states of other Two methods of calculation • “Luminosity” formula • Must measure relative luminosity (R) of up and down bunches • Separately for left and right of beam in single-transverse case • Mathematically exact • “Square-root” formula • Combine yields from up and down bunches, left and right sides of beam, so that differences in lumi of up and down bunches cancel • A (very good!) mathematical approximation C. Aidala, Indiana U., Oct. 3, 2005

  35. Beam-Beam Counters (BBC’s) • Quartz Cherenkov detectors—sensitive to forward charged particles • 3.0 < |h| < 3.9 • Determine event vertex (resolution ~2 cm) • Serve as minimum-bias (MB) trigger • 2p azimuthal coverage • Essential to avoid bias in transverse collisions, where azimuthal asymmetries are expected! • Used to measure absolute luminosity, necessary for cross-section measurements • See ~50% of total inelastic p+p cross section • Used to measure relative luminosity (R) between bunches with up and down polarization C. Aidala, Indiana U., Oct. 3, 2005

  36. Obtaining the Polarization • Only proton-carbon (pC) polarimeter available in 2001-02 • 35% total polarization uncertainty due to uncertainty in the original measurement of the polarimeter analyzing power at 22 GeV and uncertainty on energy dependence between 22 and 100 GeV • With hydrogen-jet polarimeter now available, future measurements will have 5-10% polarization uncertainty Note that any uncertainty on the polarization becomes a scale uncertainty on AN, affecting asymmetries and statistical uncertainties in the same way, preserving each point’s significance from zero C. Aidala, Indiana U., Oct. 3, 2005

  37. p0  Obtaining the (Spin-Dependent) p0 Yields • 18M events used • Central spectrometer arms |h| < 0.35 • g, p0 via p0  gg • Electromagnetic calorimeter (EMCal) • Lead scintillator calorimeter (PbSc) • Lead glass calorimeter (PbGl) p0 width ~10-15 MeV/c2 C. Aidala, Indiana U., Oct. 3, 2005

  38. 2x2 Trigger in 2001-2002 run. p EMCal-RICH Trigger • 2x2 tower non-overlapping energy sum • Threshold ~ 0.8 GeV • Also used in conjunction with RICH to form an electron trigger C. Aidala, Indiana U., Oct. 3, 2005

  39. Handling Background in the p0 Asymmetry • Eliminate as much background as possible using EMCal cluster shower shape cut and charged veto • Calculate asymmetry of (signal + background) in the p0 mass window • Calculate the asymmetry of two different background regions as an estimate of the asymmetry of the background under the peak • Subtract the asymmetries Invariant mass (GeV/c2) - 50-MeV/c2 windows around the p0 peak (60-110 and 170-220 MeV/c2) - 250-450 MeV/c2 (between p0 and h) C. Aidala, Indiana U., Oct. 3, 2005

  40. Obtaining Charged Hadron Yields • 13M events used • Event vertex from BBC’s • Track reconstruction from • vertex • drift chamber • pad chambers PC3 PC3 DC DC BBC PC1 PC1 C. Aidala, Indiana U., Oct. 3, 2005

  41. Background in h+/h- Sample • Note that tracking detectors in PHENIX are outside the magnetic field • Assume track originates at event vertex, then measure momentum based on deflection angle observed at drift chamber • Low-momentum tracks that don’t originate from the vertex may be misreconstructed with higher momentum • Conversion electrons • Decay products from long-lived particles (K+-, K0L) C. Aidala, Indiana U., Oct. 3, 2005

  42. Background in h+/h- Sample (cont.) • RICH veto to eliminate electrons • Electron threshold 0.017 GeV/c • Pion threshold 4.7 GeV/c • < 1% electron contamination in final sample • Estimate decay background from long-lived particles from tracks with reconstructed pT > 9 GeV/c but that didn’t produce a hit in the RICH • < 5% in final sample C. Aidala, Indiana U., Oct. 3, 2005

  43. From Yields to Asymmetries • Keep track of fill-by-fill polarization for each beam • Polarization-corrected asymmetries obtained fill by fill, then averaged over all fills • Also correct for the range in azimuthal coverage of the central spectrometer arms by a factor of C. Aidala, Indiana U., Oct. 3, 2005

  44. AN of Neutral Pions and Charged Hadrons: Systematic Checks • Independent results from two polarized beams • Independent results from two detector arms (luminosity formula) • Comparison of square-root and luminosity formulas • Fill-by-fill stability of asymmetry • Effects of background on p0 asymmetry • Integrate over different ranges of photon-pair invariant mass • Measure and subtract asymmetry of two different background invariant-mass regions C. Aidala, Indiana U., Oct. 3, 2005

  45. AN Bunch Shufflingas a Check for Systematic Errors • Randomly assign helicity sign for each bunch crossing • Average polarization zero • Determine AN for each fill • Fit AN across all fills • Repeat many times to get distributions for fitted AN and c2 • Widths of shuffled AN distributions consistent with statistical errors assigned to physics AN • Indicates uncorrelated systematic errors smaller than statistical errors C. Aidala, Indiana U., Oct. 3, 2005

  46. AN of Mid-rapidity Neutral Pions and Charged Hadrons: Results hep-ex/0507073 Accepted to PRL AN for both charged hadrons and neutral pions at mid-rapidity consistent with zero to within a few percent. |h| < 0.35 C. Aidala, Indiana U., Oct. 3, 2005

  47. AN at Mid-rapidity to Probe Sivers and Transversity+Collins Large asymmetries observed due to valence quarks?? • PHENIX measurement of mid-rapidity p0 AN may offer insight on transversity and the Sivers effect • Current data primarily sensitive to Sivers because particle production at mid-rapidity at these transverse momentum values is mostly from gluon scattering Future measurements reaching higher transverse momentum will be dominated instead by quark scattering and thus more sensitive to transversity + Collins C. Aidala, Indiana U., Oct. 3, 2005

  48. Upcoming Transverse Spin Measurements at PHENIX • 2005 data • Similar transverse statistics to 2001-02, but expect errors to be reduced by ~3x due to higher polarization • Improved mid-rapidity measurements of p0, h+/- AN • AN of forward and backward muons from light hadron decays • AN of forward and backward neutrons at 200 and 410 GeV • 2006 or ‘07: Back-to-back jets to probe Sivers C. Aidala, Indiana U., Oct. 3, 2005

  49. Run03 -charged dn/d anti-aligned aligned 2 0  h Jet Asymmetry Due to Sivers Boer and Vogelsang, Phys.Rev.D69:094025,2004, hep-ph/0312320 • Non-zero Sivers function implies spin-dependence in kT distributions of partons within proton • Would lead to an asymmetry in Df of back-to-back jets • Trigger doesn’t have to be a jet or leading particle, but does have to be a good jet proxy • Studies being done for high-pT photon + away-side charged hadron (Schematic) C. Aidala, Indiana U., Oct. 3, 2005

  50. Summary • Understanding proton spin a fundamental question in QCD • Transverse spin structure of the proton a rapidly developing field with much remaining to be understood • Theory and experiment currently hand-in-hand • PHENIX mid-rapidity results reveal asymmetries consistent with zero • Expected to constrain gluon Sivers function (forthcoming paper by Anselmino, d’Alesio, et al.) • Present results at forward, backward, and mid-rapidity suggest large SSA’s a valence quark effect? • Variety of future measurements necessary to separate different contributions to large SSA’s and form a cohesive picture of proton transverse spin structure C. Aidala, Indiana U., Oct. 3, 2005

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