1. Columbia University Christine Aidala September 26, 2005 Studying the Transverse Spin Structure of the Proton at LANL

2. C. Aidala, LANL, Sept. 26, 20052 F2F2 Experimental Data on Proton Structure unpolarized Q 2 (GeV 2 ) polarized g1g1 Q 2 (GeV 2 )

3. C. Aidala, LANL, Sept. 26, 20053 Parton Distributions: (well known) (moderately well known) (unknown) (moderately well known) (basically unknown) Spin Structure of the Proton: Status

4. C. Aidala, LANL, Sept. 26, 20054 Polarized Quark and Gluon Helicity Distributions up quarks down quarks sea quarks gluon 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. But what about the transverse spin structure of the proton?

5. C. Aidala, LANL, Sept. 26, 20055 Quark Distributions and Helicity Elastic proton-quark scattering (related to inelastic scattering through optical theorem) Three independent pdf’s corresponding to following helicity states: Take linear combinations to form: Helicity average Helicity difference Helicity flip 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.

6. C. Aidala, LANL, Sept. 26, 20056 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 k T and orbital angular momentum

7. C. Aidala, LANL, Sept. 26, 20057 Hard Scattering Process X q(x 1 ) g(x 2 ) 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)Universality

8. C. Aidala, LANL, Sept. 26, 20058 Mid-rapidity Cross Section Measurements NLO pQCD consistent with data within theoretical uncertainties. PDF: CTEQ5M Fragmentation functions: Kniehl-Kramer-Potter (KKP)Kniehl-Kramer-Potter (KKP) Kretzer Spectrum constrains D(gluon  ) fragmentation function Important confirmation of theoretical foundation for spin program Factorization applicable, with small scale dependence hep-ex/0507073 Accepted to PRL |  | < 0.35 9.6% normalization error not shown PRL 91, 241803 (2003) |  | < 0.35 00

9. C. Aidala, LANL, Sept. 26, 20059 k T -dependent pdf’s and FF’s Collinear factorization—assumes partons have momentum collinear to parent hadron –pdf’s and FF’s integrated in k T Allowing k T dependence to remain yields several possible new pdf’s and FF’s k T -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 k T dependence in pQCD

10. C. Aidala, LANL, Sept. 26, 200510 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 (  g) Sea-quark polarization Advantages of a polarized hadron collider –High energy  factorization, new probes (W’s) –Polarized hadrons  gq, gg collisions

11. C. Aidala, LANL, Sept. 26, 200511 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

12. C. Aidala, LANL, Sept. 26, 200512 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 RHIC as a Polarized p-p Collider Various equipment to maintain and measure beam polarization through acceleration and storage

13. C. Aidala, LANL, Sept. 26, 200513 Siberian Snakes To Maintain Polarization STAR PHENIX AGS LINAC RHIC 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

14. C. Aidala, LANL, Sept. 26, 200514 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

15. C. Aidala, LANL, Sept. 26, 200515 Polarimetry (cont.) E950 experiment at AGS became RHIC pC polarimeter –Measure P beam to ~30% H jet polarimeter expected to determine P beam to 6-8% for 2005 data Both use asymmetries in processes that are already understood to determine the beam polarization recoil proton or Carbon scattered proton polarized proton target or Carbon target (polarized) proton beam

16. C. Aidala, LANL, Sept. 26, 200516 RHIC’s Experiments Transverse spin only (No rotators) Longitudinal or transverse spin

17. C. Aidala, LANL, Sept. 26, 200517 The PHENIX Detector 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 Philosophy: High rate capability & granularity Good mass resolution and particle ID  Sacrifice acceptance

18. C. Aidala, LANL, Sept. 26, 200518 2001-02 Au+Au Au+Au and d+Au Collisions in the PHENIX Central Arms 2002-03 d+Au p+p multiplicities a tiny fraction of Au+Au!

19. C. Aidala, LANL, Sept. 26, 200519 Spin Running at PHENIX So Far 2001-2 –Transversely polarized p+p collisions –Average polarization of ~15% –Integrated luminosity 150 nb -1 –Figure of merit (P 2 L) 3.38 nb -1 2003 –Longitudinally polarized p+p collisions achieved –Average polarization of ~27% –Integrated luminosity 220 nb -1 –Figure of merit (P 4 L) 1.17 nb -1 2004 –5 weeks commissioning, 4 days data-taking –Average polarization ~40% –Integrated luminosity 75 nb -1 –Figure of merit (P 4 L) 1.92 nb -1 2005 –Average polarization ~48% –Integrated longitudinal lumi 3.59 pb -1 –Figure of merit (P 4 L) ~1.9 pb -1 –Integ. transverse lumi 0.163 pb -1 –Figure of merit (P 2 L) 0.038 pb -1

20. C. Aidala, LANL, Sept. 26, 200520 Proton Spin Structure at PHENIX Prompt Photon Production Heavy Flavors

21. C. Aidala, LANL, Sept. 26, 200521 Transverse Single-Spin Asymmetries A N 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 E704 at Fermilab at  s=19.4 GeV, p T =0.5-2.0 GeV/c: left right

22. C. Aidala, LANL, Sept. 26, 200522 Transverse Single-Spin Asymmetries (cont.) General form for transverse SSA’s: –Collinear momenta would produce no effect –Thus importance of k T Spin could be of initial proton or struck quark Possible momenta include initial proton momentum, final-state particle or jet momentum, k T of parton within proton, k T of final-state particle with respect to jet axis Lots of combinations possible!

23. C. Aidala, LANL, Sept. 26, 200523 Sivers Effect Spin-dependent intrinsic transverse momentum of the partons –Sivers (k T -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

24. C. Aidala, LANL, Sept. 26, 200524 Collins Effect Fragmentation of a transversely polarized quark into a spinless hadron has an azimuthal dependence –Collins (k T -dependent) FF Requires non-zero transversity  q(x) L=1 Collins effect (fragmentation) Collins animation: collins_animation.htm

25. C. Aidala, LANL, Sept. 26, 200525 Quark-Gluon Correlations Spin-dependent quantum correlations between quarks and gluons in the hadron Possible in either the initial state (distribution function) or final state (fragmentation function) Notable work by Qiu and Sterman, Koike Debate within theoretical community about relation to other mechanisms –Initial-state correlations equivalent to Sivers effect?

26. C. Aidala, LANL, Sept. 26, 200526 Large SSA’s Persist at RHIC Energies: STAR Forward  0 Results = 3.7 PRL 92 (2004) 171801 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!

27. C. Aidala, LANL, Sept. 26, 200527 ANAN x F *100 Transverse Single-Spin Asymmetries for  +,  -, and Proton Production at BRAHMS Preliminary x F < 0 Raw asym Preliminary Raw asym p T (GeV/c) protons Note STAR also measured zero asymmetry for  0 production at negative x F

28. C. Aidala, LANL, Sept. 26, 200528 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) A N =  0.110±0.015 preliminary

29. C. Aidala, LANL, Sept. 26, 200529 Neutron Asymmetry vs.   (Raw Asymmetry) / (beam pol.) Vertical polarization  Radial polarization

30. C. Aidala, LANL, Sept. 26, 200530 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!

31. C. Aidala, LANL, Sept. 26, 200531 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

32. C. Aidala, LANL, Sept. 26, 200532 A N of Mid-rapidity Neutral Pions and Charged Hadrons at PHENIX x F ~ 0.0 –Compare to STAR x F > 0.2, BRAHMS x F > 0.15 –First mid-rapidity results from RHIC 2001-02 data  0 : 1 < p T < 5 GeV/c h +, h - : 0.5 < p T < 5 GeV/c

33. C. Aidala, LANL, Sept. 26, 200533 Measuring A N at PHENIX 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 Consider polarization and spin states of one beam, average over spin states of other

34. C. Aidala, LANL, Sept. 26, 200534 Beam-Beam Counters (BBC’s) Quartz Cherenkov detectors—sensitive to forward charged particles 3.0 < |  | < 3.9 Determine event vertex (resolution ~2 cm) Serve as minimum-bias (MB) trigger 2  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

35. C. Aidala, LANL, Sept. 26, 200535 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 A N, affecting asymmetries and statistical uncertainties in the same way, preserving each point’s significance from zero

36. C. Aidala, LANL, Sept. 26, 200536    Obtaining the (Spin-Dependent)  0 Yields 18M events used Central spectrometer arms |  | < 0.35 –  0 via  0  –Electromagnetic calorimeter (EMCal) Lead scintillator calorimeter (PbSc) Lead glass calorimeter (PbGl)  0 width ~10-15 MeV/c 2

37. C. Aidala, LANL, Sept. 26, 200537 EMCal-RICH Trigger 2x2 tower non- overlapping energy sum Threshold ~ 0.8 GeV Also used in conjunction with RICH to form an electron trigger 2x2 Trigger in 2001-2002 run. 

38. C. Aidala, LANL, Sept. 26, 200538 Handling Background in the  0 Asymmetry Invariant mass (GeV/c 2 ) - 50-MeV/c 2 windows around the  0 peak (60-110 and 170-220 MeV/c 2 ) - 250-450 MeV/c 2 (between  0 and  ) Eliminate as much background as possible using EMCal cluster shower shape cut and charged veto Calculate asymmetry of (signal + background) in the  0 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

39. C. Aidala, LANL, Sept. 26, 200539 Obtaining Charged Hadron Yields 13M events used Event vertex from BBC’s Track reconstruction from –vertex –drift chamber –pad chambers BBC PC1 PC3 DC

40. C. Aidala, LANL, Sept. 26, 200540 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 +-, K 0 L )

41. C. Aidala, LANL, Sept. 26, 200541 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 p T > 9 GeV/c but that didn’t produce a hit in the RICH –< 5% in final sample

42. C. Aidala, LANL, Sept. 26, 200542 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

43. C. Aidala, LANL, Sept. 26, 200543 A N 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  0 asymmetry –Integrate over different ranges of photon-pair invariant mass –Measure and subtract asymmetry of two different background invariant-mass regions

44. C. Aidala, LANL, Sept. 26, 200544 Bunch Shuffling as a Check for Systematic Errors Randomly assign helicity sign for each bunch crossing –Average polarization zero Determine A N for each fill Fit A N across all fills Repeat many times to get distributions for fitted A N and  2 Widths of shuffled A N distributions consistent with statistical errors assigned to physics A N  Indicates uncorrelated systematic errors smaller than statistical errors ANAN

45. C. Aidala, LANL, Sept. 26, 200545 A N of Mid-rapidity Neutral Pions and Charged Hadrons: Results hep-ex/0507073 Accepted to PRL |  | < 0.35 A N for both charged hadrons and neutral pions at mid-rapidity consistent with zero to within a few percent.

46. C. Aidala, LANL, Sept. 26, 200546 A N at Mid-rapidity to Probe Sivers and Transversity+Collins PHENIX measurement of mid-rapidity  0 A N 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 Large asymmetries observed due to valence quarks??

47. C. Aidala, LANL, Sept. 26, 200547 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  0, h +/- A N –A N of forward and backward muons from light hadron decays –A N of forward and backward neutrons at 200 and 410 GeV 2006 or ‘07: Back-to-back jets to probe Sivers

48. C. Aidala, LANL, Sept. 26, 200548 Jet Asymmetry Due to Sivers Non-zero Sivers function implies spin- dependence in k T distributions of partons within proton Would lead to an asymmetry in  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-p T photon + away- side charged hadron 00 22  h Boer and Vogelsang, Phys.Rev.D69:094025,2004, hep-ph/0312320 anti-aligned aligned Run03  -charged dn/d  (Schematic)

49. C. Aidala, LANL, Sept. 26, 200549 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

50. C. Aidala, LANL, Sept. 26, 200550 Extra Slides

51. C. Aidala, LANL, Sept. 26, 200551 pdf’s and FF’s

52. C. Aidala, LANL, Sept. 26, 200552 Single Transverse Collision Hard Scattering Process X q(x 1 ) g(x 2 )

53. C. Aidala, LANL, Sept. 26, 200553 Collins and Sivers asymmetries for leading hadrons at COMPASS COMPASS asymmetries consistent with zero Marginal Collins effect seen at large z

54. C. Aidala, LANL, Sept. 26, 200554 Sivers and Collins asymmetries at HERMES

55. C. Aidala, LANL, Sept. 26, 200555 Unpolarized Results from Run03 p+p anti-aligned aligned Asymmetry numerator is difference between aligned and anti-aligned  dist’s, where aligned means trigger jet and spin in same direction denominator is simply unpolarized  distribution On left are some theoretical guesses on expected magnitude of AN from Siver’s On right are gamma-charged hadron  dist’s from Run03 p+p 2.25 GeV gamma’s as jet trigger, 0.6-4.0 GeV charged hadrons to map out jet shape Dotted lines are schematic effect on away side  dist due to Siver’s Fn (not to scale) Run03  -charged dn/d  Boer and Vogelsang, PRD69:094025,2004

56. C. Aidala, LANL, Sept. 26, 200556 A N Reduction 2: Di-Hadron vs. Di-Jets up down unpolarized away side parton ANAN di-hadron di-jet Since we don’t reconstruct jets fully, we have to use di-hadron correlations to measure jet . This smears out the di-hadron A N relative to the di-jet A N, with smearing function g (assumed here to be a gaussian, with  jT =0.35). The effect broadens and lowers (by just a little bit) the asymmetry

57. C. Aidala, LANL, Sept. 26, 200557 RHIC Specifications 3.83 km circumference Two independent rings –Up to 120 bunches/ring –106 ns crossing time Energy: è Up to 500 GeV for p+p è Up to 200 GeV for Au+Au (per N-N collision) Luminosity –Au+Au: 2 x 10 26 cm -2 s -1 – p+p : 2 x 10 32 cm -2 s -1 (polarized)

58. C. Aidala, LANL, Sept. 26, 200558 RHIC pC Polarimeter Carbon filament target (5  g/cm 2 ) in the RHIC beam Measure recoil carbon ions at  ~90 º 100 keV < E carbon < 1 MeV E950 Experiment at AGS (1999)  RHIC polarimetry now Allows measurement of beam polarization to within 30%

59. C. Aidala, LANL, Sept. 26, 200559 Polarized Hydrogen Gas Jet Target thickness of > 10 12 p/cm 2 polarization = 93% (+1 −2)% Silicon recoil spectrometer to: Measure left-right asymmetry A N in pp elastic scattering in the CNI region to  A N < 10 -3 accuracy. Calibrate the p-Carbon polarimeters Two large data samples at 24 and 100 GeV Expect results on P Beam to 6-8% this year Courtesy Sandro Bravar, STAR and Yousef Makdisi, CAD RHIC H Jet Polarimeter Commissioned 2004

60. C. Aidala, LANL, Sept. 26, 200560 The Road to P beam with the JET target Requires several independent measurements 0 JET target polarization P target (Breit-Rabi polarimeter) 1 A N for elastic pp in CNI region: A N = 1 / P target  N ’ 2 P beam = 1 / A N  N ” 1 & 2 can be combined in a single measurement: P beam / P target =  N ’ /  N ” “ self calibration” works for elastic scattering only 3 CALIBRATION: A N pC for pC CNI polarimeter in covered kinematical range: A N pC = 1 / P beam  N ”’ (1 +) 2 + 3 measured simultaneously with several insertions of carbon target 4 BEAM POLARIZATION: P beam = 1 / A N pC  N ”” to experiments at each step pick-up some measurement errors: transfer calibration measurement expected precision

61. C. Aidala, LANL, Sept. 26, 200561 The PHENIX Collaboration 13 Countries; 62 Institutions; 550 Participants as of 3/05