Hard QCD in pp Collisions at RHIC

1. Hard QCD in pp Collisions at RHIC ECT* Workshop on Hard QCD with Antiprotons at GSI FAIR Carl A. Gagliardi Texas A&M University Outline • Unpolarized pp collisions • Longitudinally polarized pp collisions • Transversely polarized pp collisions • Looking ahead

2. RHIC: the Relativistic Heavy Ion Collider • Search for and study the Quark-Gluon Plasma • Explore the partonic structure of the proton • Determine the partonic structure of nuclei

3. Unpolarized pp collisions at RHIC • “Baseline” physics! • pp collisions provide an essential baseline to determine what’s new in heavy-ion collisions • Unpolarized pp collisions establish the applicability of pQCD to interpret results from polarized pp collisions • Unpolarized pp collisions constrain the non-perturbative inputs for pQCD calculations

4. Mid-rapidity π0 production at RHIC PRL 91, 241803 • Data favor the KKP fragmentation function over Kretzer • Mid-rapidity π0 cross section at 200 GeV is well described by pQCD over 8 orders of magnitude

5. √s=23.3GeV √s=52.8GeV Data-pQCD differences at pT=1.5GeV NLO calculations with different scales: pT and pT/2 Ed3s/dp3[mb/GeV3] Ed3s/dp3[mb/GeV3] q=5o q=10o q=15o q=53o q=22o xF xF Forward π0 production at ISR energies Bourrely and Soffer, EPJ C36, 371: NLO pQCD calculations underpredict the data at low s from ISR Ratio appears to be a function of angle and √s, in addition to pT

6. STAR Forward pp  π0 + X cross sections at 200 GeV PRL 97, 152302 • The error bars are statistical plus point-to-point systematic • Consistent with NLO pQCD calculations at 3.3 < η < 4.0 • Data at low pT trend from KKP fragmentation functions toward Kretzer. NLO pQCD calculations by Vogelsang, et al.

7. STAR Mid-rapidity protons and charged pions PLB 637, 161 • pQCD calculations with AKK fragmentation functions give a reasonable description of pion and proton yields in elementary collisions • Calculations with KKP significantly underestimate proton yields at high-pT • Protons arise primarily from gluon fragmentation; pions receive a large quark contribution at high-pT

8. BRAHMS Forward rapidity π, K, p • Charged pion and kaon yields at forward rapidity are described reasonably by a “modified KKP” fragmentation function • AKK seriously misses the forward antiproton/proton ratio (expects ~1, see ~0.05 above ~2 GeV/c) • KKP underestimates the p+pbar yield by a factor of ~10 PRL 98, 252001

9. From “tests” to tools de Florian et al, PRD 75, 114010 • RHIC data now provide important constraints for global analyses of pion fragmentation functions

10. Kaon fragmentation functions de Florian et al, PRD 75, 114010 • Also introducing important new constraints for kaon fragmentation functions

11. Proton fragmentation functions • Mid-rapidity STAR data are “the best constraint on the gluon fragmentation function into protons at large z” • Large BRAHMS forward proton to anti-proton excess “remains an open question” de Florian et al, arXiv:0707.1506

12. What about “fundamental objects”? PRL 98, 012002 • The direct photon yield is well described by pQCD

13. STAR Jets • Jet structure at 200 GeV is well understood • Mid-rapidity jet cross section is well described by pQCD over 7 orders of magnitude PRL 97, 252001

14. World Data on g1p as of 2005 All fixed-target data World DIS database with DGLAP fits Partonic structure of the proton • HERA data provide very strong constraints on unpolarized PDFs • Much less polarized DIS data; over a limited Q2 region • Gluon and sea-quark polarizations largely unconstrained by DIS

15. Origin of the proton spin? Polarized DIS: 0.2~0.3 Poorly Constrained Leader et al, hep-ph/0612360 ΔG = 0.13 ± 0.16 ΔG ~ 0.006 ΔG = -0.20 ± 0.41 • RHIC Spin program • Longitudinal polarization: Gluon polarization distribution • Transverse polarization: Parton orbital motion and transversity • Down the road: Anti-quark polarization

16. RHIC: the world’s first polarized hadron collider • Spin varies from rf bucket to rf bucket (9.4 MHz) • Spin pattern changes from fill to fill • Spin rotators provide flexibility for STAR and PHENIX measurements • “Billions” of spin flips during a fill with little if any depolarization

17. 10 20 f: polarized parton distribution functions 30 pT(GeV) Inclusive ALL measurements (0, ±, and jets) For most RHIC kinematics, gg and qg dominate, making ALL sensitive to gluon polarization.

18. -1<<2 Inclusive  -1<<2 Inclusive o -1<<2 Inclusive jet -1<<2 Inclusive  Predicted sensitivity for different ΔG scenarios Calculations by W. Vogelsang • Jets (STAR) and π0 (PHENIX and STAR) easier • γ and ALL(π+) - ALL(π-) sensitive to the sign of ΔG • Inclusive measurements average over broad x ranges Sampled x range for inclusive jets

19. STAR STAR jets from Runs 3+4PRL 97, 252001 Gluon polarization is not “really big” (GRSV-max: CL ~ 0.02)

20. STAR Charged pions from Run 5 π+ π-

21. STAR STAR neutral pions from Run 5 • ALL disfavors large (positive) gluon polarization • Energetic π0 carry a significant fraction of the total transverse momentum of their associated jet z Mean ratio of 0 pT to Jet pT π0

22. PHENIX neutral pions from Run 5arXiv:0704.3599 • χ2 from a comparison to the GRSV polarized parton distributions • Uncertainties associated with GRSV functional form not included • Large positive polarizations excluded; large negative polarizations disfavored

23. STAR STAR jets from Run 5 • CL from a comparison to the GRSV polarized parton distributions • Uncertainties associated with GRSV functional form not included • Large positive polarizations excluded; large negative polarizations disfavored • Uncertainties from Run 6 will be a factor of ~3 smaller at high pT g = g (max) g = -g (min) g = 0 GRSV-STD 2005 STAR preliminary

24. PHENIX π0 from Run 6 • Preliminary Run 6 χ2 comparison, including statistical uncertainties only (syst. are expected to be small) • Its looking like ΔG is quite small or negative

25. STAR Single-spin asymmetries at forward rapidity PRL 92, 171801 • Large single-spin asymmetries at CM energies of 20 and 200 GeV • Weren’t supposed to be there in naïve pQCD • May arise from the Sivers effect, Collins effect, or a combination

26. Transverse momentum dependent distributions exist Sivers Collins SIDIS can distinguish transverse motion preferences in PDF’s (Sivers) vs. fragmentation fcns. (Collins) HERMES results  both non-zero. + vs. – differences suggest opposite signs for u and d quarks.

27. Sivers effect in di-jet production J. Balewski (IUCF) Sivers effect: Sivers ON spin 1 • Left/right asymmetry in the kT of the partons in a polarized proton • Spin dependent sideways boost to di-jets • Requires parton orbital angular momentum  > 180 for kTx > 0 di-jet bisector kTx 2

28. STAR Sivers di-jet measurementarXiv:0705.4629 • Measure the di-jet opening angle as a function of proton spin • Both beams polarized, xa  xb  pseudorapidity dependence can distinguish q vs. g Sivers effects. Mostly: +z beam quark −z beam gluon

29. STAR Sivers di-jet measurementarXiv:0705.4629 • Observed asymmetries are an order of magnitude smaller than seen in semi-inclusive DIS by HERMES • Detailed cancellations of initial vs. final state effects and u vs. d quark effects?

30. BRAHMS BRAHMS forward rapidity pion measurements at 200 GeV • Sign dependence of charged pion asymmetries seen in FNAL E704 persists to 200 GeV 4 deg (~3) 2.3 deg (~3.4)

31. BRAHMS Additional BRAHMS forward rapidity results at 200 GeV 2.3 deg (~3.4) • Charged kaon AN both positive; slightly smaller or comparable to π+ • Antiprotons show a sizable positive AN • Protons show little asymmetry

32. BRAHMS BRAHMS results at 62.4 GeV Combined results from 2.3 and 3 deg • Lower beam energy • Larger xF • Very large asymmetries! Limitation of the BRAHMS measurements: Very strong correlation between xF and pTfrom small acceptance

33. STAR Inclusive forward  asymmetry, AN Data Theory Kouvaris et al, hep-ph/0609238 Decreasing η Increasing pT The data show exactly the opposite behavior

34. STAR AN(pT) in xF-bins • Combined data from three runs • at <η>=3.3, 3.7 and 4.0 • In each xF bin, <xF> does not • significantly changes with pT • Measured AN is not a smooth • decreasing function of pT • as predicted by theoretical • models Kouvaris et al, hep-ph/0609238

35. Separating Sivers and Collins effects Sivers mechanism:asymmetry in the forward jet or γ production Collins mechanism:asymmetry in the forward jet fragmentation SP SP kT,q p p p p Sq kT,π Sensitive to proton spin – parton transverse motion correlations Sensitive to transversity • Need to go beyond inclusive π0 to measurements of jets or direct γ • Have some Run 6 data under analysis • Will study in Run 8 with the STAR Forward Meson Spectrometer

36. STAR Forward Meson Spectrometer South half of FMS array during assembly • Pb glass calorimeter covering 2.5 < η < 4 • Detect direct photons, jets, di-jets, ….. in addition to π0, for kinematicswhere π0 single-spin asymmetries are known to be large

37. Looking beyond inclusive ALL measurements • Inclusive ALL measurements at fixed pT average over a broad x range. • Need a global analysis to determine the implications • Can hide considerable structure if ΔG(x) has a node

38. The next few years: ΔG(x) • Di-jets access LO parton kinematics • Involve a mixture of qq, qg, and gg scattering STAR (pre-)preliminary 2005 Data Simulation

39. γ + jet events • γ + jet provides very good event-by-event determination of the parton kinematics • 90% of the yield arises from qg scattering • Can choose the kinematics to maximize the sensitivity to ΔG(x)

40. Down the road: anti-quark polarization • With two polarized beams and W+ and W-, can separate u, d, u, d polarizations • These simulations are for the PHENIX muon arms • STAR will do this with electrons • Need 500 GeV collisions at high luminosity, and upgrades to both PHENIX and STAR

41. Further future: spin measurements in the RHIC II era Direct measurement of the Δs, Δs contributions in charm-tagged W boson production Sivers asymmetry AN for Drell-Yan di-muon and di-electron production

42. Conclusion • pp collisions at RHIC are providing important new inputs for our understanding of fragmentation functions • The world’s first polarized hadron collider is generating a wealth of new data regarding the spin structure of the proton • We’ve only barely started!

44. 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