Spin Physics With Jets at STAR

1. Spin Physics With Jets at STAR f S. Vigdor, BNL, Ides of March 2007 • RHIC Spin Goals • RHIC Spin Infrastructure • STAR Jet Infrastructure • Inclusive Jet Results 2003-5: Constraining the Gluon Contribution to Proton Spin • Single-Spin Asymmetry for Di-jets 2006: Looking for Parton Orbital Momentum Effects • Next Stages of Jet Program

2. Nucleon Structure Goal: How are Various Degrees of Freedom Interrelated? Chiral symmetry breaking associated with pseudoscalar meson cloud  d/u asymmetry, sea-quark orbital motion, sea quark spin opposes nucleon’s. ¯ ¯ u u d u u Hard high-energy probes sample light-cone wave function, provide momentum & spin “snapshots” of teeming assembly of partons  ¯ d d d + n Szp = ½ = ½  + g + Lzquarks + Lzgluons gluon helicity quark helicity How do these quantities relate to above pictures? Three constituent quarks in s-states  good account for baryon magnetic moments -- attributes nucleon spin to quark spin alignment in rest-frame wave function.

3.   RHIC p+p  Unique Insights Into Selected Questions  Access to spin observables in hard partonic scattering processes treatable via perturbative QCD  probe non-perturbative nucleon spin structure via partonic degrees of freedom: • Do gluons account for “missing” proton spin? Gluons provide ~ half of proton’s mass, momentum; do they also play important role in spin? If not g, then orbital contributions! • Transverse quark motion and spin preferences in transversely polarized nucleon? Transverse motion  orbiting mesons? Transverse spin decoupled from gluons, relativistically distinct from helicity preferences. • Gluon splitting vs. Goldstone bosons and flavor-dependent sea quark polarization? Jet production studies illuminate first two major questions!

4. RHIC Spin Infrastructure

5. RHIC  Riken-BNL Helicity-Identified Collider RHIC pC Polarimeters Absolute Polarimeter (H jet) BRAHMS PHOBOS Absolute Pbeam calibration to ~ 5% goal in Siberian Snakes Siberian Snakes progress PHENIX STAR Spin Rotators (longitudinal polarization) Spin flipper Spin Rotators (longitudinal polarization) Solenoid Partial Siberian Snake Pol. H- Source Helical Partial Siberian Snake LINAC BOOSTER AGS Internal Polarimeter AGS 200 MeV Polarimeter AGS pC Polarimeters Strong Helical AGS Snake Rf Dipole Cold Siberian snake in AGS, March 31, 2005 Pioneering accelerator development  unique spin capabilities! RHIC uses super-conducting helical dipole magnets for Snakes and spin rotators Polarization survival has been demonstrated to 250 GeV beam momentum (from 24 GeV injection)

6. Steady Improvements in Polarized Beam Performance May 2006 May 2006 2006 delivered pp  L dt 2003  2006  > 2 orders of magni-tude improvement in P 4L relevant to 2-spin asym-metries! STAR  s = 200 GeV pp Sampled Luminosities Factor ~ 5--6 remains to reach “enhanced design” goals

7. The Beam Polarization Monitoring Chain Jet pol CNI pol BBC pol

8. STAR Jet Infrastructure

9. Detector Lum. Monitor Local Polarim. Barrel EM Calorimeter -1<η< 1 +y +x +z STAR 2003 2004 2005 Triggering Beam-Beam Counters 2<|η|< 5 h = - ln(tan(q/2) h=0 h= -1 WEST EAST h=2 Triggering Endcap EM Calorimeter Forward Pion Detector 1<η< 2 -4.1<η< -3.3 Time Projection Chamber -2<η< 2 Solenoidal Magnetic Field 5kG Tracking

10. STAR Barrel EMC (Wayne State U. + …) … in HI as well as p+p collisions! STAR Forward Pion Detector (BNL + …) STAR Endcap EMC (Indiana U. + ANL + …) EMC’s Essential for the Spin Program and Jet Detection p+p Di-jet event in BEMC STAR barrel (completed 2006), endcap (completed 2005) and forward (upgraded 2006) em calorimeters permit triggering/reconstruc-tion for jets, , 0, … STAR central Au+Au

11. Jet Energy Scale Relies on EMC Calibration Set E-scale using 1.8<p<8 GeV/c electrons Single Tower MIP Relative gain of every tower (4800 for BEMC, 720 for EEMC) determined from MIP response. Identify MIP’s via tracks for BEMC, via SMD + preshower + postshower response for EEMC Absolute E scale set by comparison to track momentum for identified electrons Cross-check from reconstructed  0 invariant mass. Overall gain precision =  5% presently. Aim for 2% in near future.

12. Jet Triggering in STAR +13,…,18 7 1 8 12 2 jet patch 3 size:1x1  x  11 9 4 10 4 8 1x1 Jet patch ET/GeV Trigger either on HT:  1 (of 4800 BEMC or 720 EEMC) tower ET > thresh. Or JP:  1(of 12 BEMC or 6 EEMC) hard-wired jet patch  ET > thresh. 2006 rate ~ 150 Hz, combine with L2 trigger to fit in limited bandwidth 2006 rate ~ 2.5 Hz, sent to tape without prescaling Allocated Jet Rate to tape: ~15 Hz

13. Jet Reconstruction in STAR • Use “midpoint-cone” algorithm (hep-ex/0005012): • Search over all possible seeds (pTseed > 0.5 GeV) for stable groupings • Check midpoints between jet-jet pairs for stable groupings • Split/merge jets based on Eoverlap • Add all track/tower 4-momenta Data Simulation detector “geant” jets GEANT “pythia” jets particle • Use cone radius: • = 0.4 for half-BEMC 2003-5 • = 0.7 for full B+EEMC 2006 pythia parton theory • Correction philosophy: • PYTHIA+GEANT  detector response • Use to correct for “particle”  “detector” effects of resolution, efficiency, bias • PYTHIA also  study “parton”  “particle” effects of hadronization, event energy

14. Simulations Use Same EMC Status Tables as Data Analysis to Reproduce Details of Response High tower trigger pt (jet) >10 GeV/c Red  pythia + gstar Black  2004 data All error bars statistical 2004 Fraction of jet pT in sub-cone of radius r BEMC tower size BEMC tower size Efficiency dips between jet patches, sometimes enhanced by FEE hardware problems, reflected in status tables Observed jet shapes well reproduced

15. Subtleties of Jet Analysis: Jet Energies data simulation Detector jet pT Error bars reflect rms spread of simulated detector jet pT in given bin of particle jet pT Steep pT spectrum + crude jet energy resolution  detector jets spawned, on average, by lower-pT particle jets (despite loss of neutral hadrons w/o hadron calorimeter). Simulation + di-jet data analysis  resolution /pT  25% Simulation Log yield pT (measured) • pT shift incorporated to date by cross section corrections, ALL syst. errors • Future pubs. to correct E scale, with uncertainties in horizontal errors • “Particle”  “detector” jet shift  same for gg vs. qg vs. qq • “Parton”  “particle” shifts from hadronization (E loss) and underlying event (E gain) are subprocess-dependent, to be incorporated in syst. errors

16. Subtleties of Jet Analysis: Trigger Bias Fake jets from upstream beam bkgd. Shaded bands = simulations EMF  Electromagnetic Energy Fraction   ET(EMC) / total jet pT • High Tower and Jet Patch triggers require substantial fraction of jet energy in neutral hadrons • Trigger efficiency turns on slowly above nominal threshold • Efficiency differs for quark vs. gluon jets, due to different fragmentation features Simulations reproduce measured bias well, except for beam background at extreme EM energy fraction • Conclude: • Cut out jets at very high or very low EMF • Use simulations to estimate syst. errors from trigger bias

17. Inclusive STAR Jet Results 2003-5

18. Published Jet Production Cross Sections (2003+4) Rely on Simulated Correction Factors “measured” Simulation “true” εjet : decreases c(pT) resolution: increases c(pT) εTrig: ~1 e-2 at pT-jet = 5 GeV ~1 at pT-jet = 50 GeV • Jet pT resolution ~ 25% • HT efficiency changes by 2 orders of magnitude! • Consistent results from both PYTHIA and HERWIG

19. Early RHIC pp Absolute Cross Section Results PHENIX pp  0X s=200 GeV Mid-rapidity STAR pp  jet+X, s=200 GeV Mid-rapidity PHENIX Prelim-inary pp  X s=200 GeV STAR pp  0X, s=200 GeV High rapidity Syst. Unc. dominated by jet E scale uncertainty pQCD works! Absolute cross sections for channels critical to gluon polariza-tion determination -- p+p  0+X, jet + X,  +X at  s = 200 GeV– arewell repro-duced in NLO pQCD calcs. down to pT ~ few GeV/c. Low-pT reach of robust pQCD account was not anticipated!

20. Current Info on Unpolarized Quark & Gluon Distrib’ns Parton Model  F2p(x,Q2) =  ei2 x [qi (x,Q2) + qi (x,Q2)] xf(x) for quarks & gluons in proton from current fits to world PDF database xf(x,Q2=10 GeV2) Gluons World DIS database with DGLAP fits g(x,Q2) from scaling violations in F2

21. Polarized DIS Data Are Too Sparse to Constrain Gluon Helicity Preferences Well: World Data on g1p as of 2005 Parton Model g1p = ½ ei2 [qi (x,Q2) + qi (x,Q2)] Only ~20-30% of proton spin arises from q and q helicity preferences ! Only valence quarks are strongly polarized All fixed-target data limited info on scaling violations,  on shape or integral of gluon helicity preferenceg(x,Q2).

22.   Constraining g Via p+p  jet + X Spin Correlations pp  hX “soft” parton distribution functions pQCD factoriz’n  “soft” frag. function ∧ “hard” dQCD parton-parton Fragmentation functions not needed for jet calcs. Theory ingredients: pQCD factorization + LO + NLO pQCD 2-spin asymmetries

23. STAR 2005 Inclusive Jet ALL Results STAR Preliminary 2005 1.0 Inclusive Jets: LO (W. Vogelsang) 0.8 0.6 qg Fraction of Cross Section 0.4 qq gg All HT & JP triggers combined  1.97M events 0.2 0 10 15 20 25 30 0 5 pTjet (GeV/c) 3.1 pb1 sampled  1.6 pb1 after run selection; PBPY  0.25 • Ongoing analysis is: • recovering more runs • correcting to particle jet E scale • reducing systematic errors • quantifying constraint on g Results do not support g(1.0GeV2) much > 0.4 within GRSV shape ansatz

24. pp  0 +X @ s=200 GeV ALL STAR 2005 Inclusive Jet ALL Results are Consistent Among Different Jet Triggers, and With 2003+4 STAR Results and 2005+6 PHENIX ALL for Inclusive  0

25. Inclusive Jet Data from 2006 Will Provide Far Greater Discriminating Power for g DG=G GRSV-std DG=-G DG=0 Projected statistical uncertainties for STAR 2006 inclusive jet ALL xgluon Inclusive 0 200 500 101 GeV N.B. x-range sampled depends on g(x,Q2) ! -- M. Stratmann 102 0 10 30 20 pT (GeV) • High-statistics (esp. at high pT) inclusive jet and 0ALL data from 2006 will select among g models, assuming a shape of g(x,Q2). • Inclusive channels suffer from integration over x  model-dependent Gextraction. • With improved beam & detector performance, focus is now shifting to jet-jet and  -jet coincidences for event-by-event constraints on colliding parton x1,2:

26. Single-Spin Asymmetry for Di-Jets 2006

27. Sizable Transverse Single-Spin Asymmetries Seen for Forward Hadron Production p+p  hadron + X, s = 200 GeV lab = 4.0 lab = 2.3 Similar to SSA seen in FNAL E704 @ s = 20 GeV, but here in regime where pQCD accounts for cross section!

28. Transverse Spin Measurements Have Stimulated Rapid Development of Theory sproton pproton a) Partons in the initial state -- Sivers effect: Sensitive to parton orbital components in proton wave function, but also needs initial- and/or final-state interactions to evade TRV. kTparton ? pQCD Non-pert. Non-pert. Factorization: kTparton ?  Hard hadronic d = PDF’s  hard partonic d  fragment’n fcn. b) Hadrons emerging off-axis in quark  jet fragmentation -- Collins effect: Requires quark transverse spin orientation preference in transversely polarized proton (“transversity”) + spin transfer to outgoing quark in pQCD scattering. • Observed AN values orders of magnitude too large to arise from explicit chiral-symmetry breaking quark mass terms in QCD Lagrangian. • Steep pT -dependence of d  sensitivity to spin-correlated transverse momentum preferences in non-perturbative factors:

29. Distinguishing Sivers from Collins Asymmetries Sivers Collins In SIDIS, can distinguish transverse motion preferences in PDF’s (Sivers) vs. in fragmentation fcns. (Collins) via asym. dependence on 2 azimuthal angles: HERMES results  both non-zero, but  + vs. – difference suggests Sivers functions opposite for u and d quarks.

30. Motivation for pp  Di-Jet Measurement • HERMES transverse spin SIDIS asymmetries  u and d quark Sivers functions of opposite sign, different magnitude. • Sivers effect in pp  spin-dependent sideways boost to di-jets, suggested by Boer & Vogelsang (PRD 69, 094025 (2004)) • Both beams polarized, x +z  x z  can distinguish high-x vs. low-x (primarily gluon) Sivers effects. • Do we observe q Sivers consistent with HERMES, after inclusion of proper pQCD-calculable ISI/FSI gauge link factors for pp  jets? Tests universality. • First direct measurement of gluon Sivers effects. y proton spin x z Colliding beams parton kTx

31. STAR EMC-Based (Level 0 + 2) Di-Jet Trigger in 2006 • 2006 p+p run, 1.1 pb1 • 2.6M di-jet triggered events • 2 localized clusters, with ETEMC > 3.5 GeV, | | > 60 Reco cos(bisector) measures sign of net kTxfor event Endcap essential for q vs. g Sivers distinction spin Jet 1   bisector Jet 2  EMC Barrel  = -1 EMC Endcap TPC  =+2 BBC East BBC West Blue (+z) Yellow (-z) beam Full, symmetric 1,2 coverage Broad 1,2 coverage Is -distribution narrow enough for precise determination of centroid ? Signed azimuthal opening angle 

32. EMC-Only Information OK For 1st Dijet Sivers Asymmetry • Jet finder • TPC+EMC • jet cone radius 0.6  (full reco) –  (L2) [deg] Net L2-to-parton (jet) = 6.3, (di-jet) = 9.0 Full offline di-jet reconstruction for ~2% of all runs shows triggered jet pTspectrum: Typical xT ~ 0.05 - 0.10; 1+2 range  0.01 < xBj < 0.4 and  angle resolution loss @ L2 OK: [()=3.9, ()=5.8] L2 vs. full jet << observed()  20, mostly from kT PYTHIA+GEANT  full jet reconstruction vs. parton-level resolution: [()=5.0, ()=0.10] full reco. jet vs. parton angles

33. Fast MC Simulations Illustrate Di-Jet Sivers Effects f = 0.85 dilution corrected in data • random kTx,y (rms = 1.27 GeV/c) for each parton • Sivers spin-dep. kTx offset   shift, L-R di-jet bisector asym. • 1-spin effects vary linearly with kTx offset • 2-parton events, transverse plane • match full jet reco. pT distribution • Gaussian + exp’l tail kT distribution fits  distribution

34. STAR Results Integrated Over Pseudorapidity Null Tests STAR data both jets rotated by 90 AN-z AN-z AN+z AN+z 2-spin 2-spin  rotation samples kTy, parity-violating sp•kT correl’n Error-weighted avg. of 16 independent AN(>) values for |cos(bisector)| slices, with effective  beam polarization for each = Pbeam |cos(bisector)| • Sivers asymmetries consistent with zero with stat. unc. = 0.002 • Fast MC  sensitivity to Sivers kTx offset  few MeV/c  0.002 (kTx)21/2 • Systematic uncertainties smaller than statistics • All null tests, including forbidden 2-spin asym.  cos(bisector), consistent with zero, as are physics asymmetries for all polarization fill patterns • Validity of spin-sorting confirmed by reproducing known non-zero AN for inclusive forward charged-particle production (STAR BBC’s)

35. What Did We Expect? Constraints from SIDIS Results Fits to HERMES SIDIS Sivers asymmetries constrain u and d quark Sivers functions, for use in pp  dijet + X predictions. Jet 1 rapidity Jet pT (GeV/c) E.g., Vogelsang & Yuan use two different models of Sivers fcn. x-dependence: W. Vogelsang and F. Yuan, PRD 72, 054028 (2005). • Dijet calcs. include: • no hadronization • no gluon Sivers fcns. • 5 < pTparton < 10 GeV/c • Initial-state interactions only (à la Drell-Yan) • Trento sign convention (opposite Madison) 1 jet forward, expected |AN| ~ 0.1, little pT - dep.

36. Theory of Transverse SSA Developing Very Rapidly! VY 2 SIDIS Sivers fit FSI only ISI+FSI ISI only Bomhof, Mulders, Vogelsang & Yuan, hep-ph/0701277 Sivers fcns. from twist-3 qg correl’n fits to pp  forward hadron • Ji, Qiu, Vogelsang & Yuan [PRL 97, 082002 (2006)] show strong overlap between Sivers effects & twist-3 quark-gluon (Qiu-Sterman) correlations: • twist-3 fits to AN(p+p  fwd. h) can constrain Sivers fcn. moment relevant to weighted di-jet SSA • Kouvaris et al. [PRD 74, 114013 (2006)] fits give nearly complete u vs. d cancellation in weighted di-jet SSA d quark u+d u quark Bomhof, Mulders, Vogelsang & Yuan, hep-ph/0701277 Di-jet SSA Post-dictions shrinking! Bacchetta, Bomhof, Mulders & Pijlman [PRD 72, 034030 (2005)] deduce gauge link structure for pp  jets, hadrons:  AN (ISI+FSI)   0.5 AN (ISI)  Gauge links more robust for SSA weighted by  pT for 2 jets, or |sin  |

37. STAR Di-Jet Sivers Results vs. Jet Pseudorapidity Sum Blue beam Yellow beam STAR AN all consistent with zero  both net high-x parton and low-x gluon Sivers effects ~10x smaller in pp  di-jets than SIDIS quark Sivers asym.! • All calcs. for STAR  acceptance • Reverse calc. AN signs for Madison convention • Scale Bomhof calcs by 1/|sin |  3.0 to get AN of unit max. magnitude • u vs d and FSI vs ISI cancellations  sizable SSA in inclusive fwd. h prod’n and SIDIS (weighted SSA) compatible with small weighted di-jet SSA -- test via LCP flavor select

38. 2006 L2 di-jet EMC  acceptance Next Stages of STAR Jet Spin Program 2 1 (1– 2)/2 = tanh –1(cos *) 0 -1 -2 0.6 Vogelsang & Yuan pQCD, pT = 5 - 10 GeV/c 0.5 0.4 Parton Subprocess Fraction 0.3 0.2 0.1 0 -2 -1 0 1 2 3 4 (1 + 2) = ln (xa /xb) • Transverse spin: • Full jet reconstruction for 2006 di-jets for pT - sorting, leading hadron charge determ. for flavor selectivity • New Forward ( = 2.5 - 4) Meson Spectrometer extends coverage to region where large inclusive AN seen Longitudinal spin: to be expanded by FMS! • Exploit full di-jet kinematic range to enhance sensitivities: • E.g., 1  2 > 1 enhances qg scattering sensitivity to g(low x) • High pT, large |1  2|, 1 + 2  0, HT trigger enhances qq sensitivity to test pQCD

39. 2006-10: Coincidence Measurements to Map g(x) Fully • E.g., detect -jet coincidences in polarized proton collisions at s = 200 and 500 GeV • Measure two-spin asymmetry in production rates between equal vs. opposite helicities, as function of (jet), (), pT ( ) • Assuming 2-body parton kinematics, can infer initial x values of gluon and quark • Next-Leading-Order (NLO) pQCD analyses of data, with DIS database, can extract g(x) for Q2 ~ 100 GeV 2 • LO pQCD analysis of simulations at right  STAR sensitivity for 3 diff. models of initial gluon helicity distributions

40. Summary & Conclusions • STAR jet spin program is well under way, fueled by ample cross sections, large STAR acceptance & efficient EMC triggering. • NLO QCD describes cross section well over 7 orders of magnitude. • Inclusive jet ALL beginning to provide best constraints on gluon polarization in the proton. 2006 data will  dramatic improvement. • Di-jet ANSivers all consistent with zero  compatible with sizable AN for inclusive forward hadrons and SIDIS? Add flavor enhancement to test u vs. d cancellation. • Early successes  shift focus now to: • Improve EMC calibration and quantitative understanding of syst. errors from energy scale ambiguities, trigger/reconstruction bias • Extend coincidence acceptance with Forward Meson Spectrometer • Exploit full kinematic characterization of parton scattering in di-jet and  - jet coincidences to enhance interpretation of gluon polarization and transverse motion preferences in polarized proton • Extend measurements to 500 GeV c.m. energy  smaller x

41. Backup Slides

42. Theory Systematics Changing the pdf Changing the scale

43. Jet Energy Scale Systematics * Included in Correction Factor