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k T Asymmetry in Longitudinally Polarized p + p Collisions at PHENIX

k T Asymmetry in Longitudinally Polarized p + p Collisions at PHENIX. October 6, 2008 Douglas Fields. Measuring jet k T – di-hadron correlation.  o - h ± azimuthal correlation.

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k T Asymmetry in Longitudinally Polarized p + p Collisions at PHENIX

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  1. kT Asymmetry in Longitudinally Polarized p+p Collisions at PHENIX October 6, 2008 Douglas Fields

  2. Measuring jet kT– di-hadron correlation o- h±azimuthal correlation Trigger on a particle, e.g. o, with transverse momentum pTt. Measure azimuthal angular distribution w.r.t. the azimuth of associated (charged) particle with transverse momentum pTa. The strong same and awayside peaks in p-p collisions indicate di-jet origin from hard scattering partons. kT Asymmetry in Longitudinally Polarized p+p Collisions at PHENIX - UVa - SPIN 2008

  3. Origin of Jet kT Net transverse momentum of a di-hadron pair in a factorization ansatz kT Another Possibility: • Spin-correlated transverse momentum – partonic orbital angular momentum • Can examine the helicity dependence of each term: Di-hadron pT • initial – e.g., fermi motion of the confined quarks or gluons, initial-state gluon radiation… • hard – final-state radiation (three-jet)… • frag – fragmentation transverse momentum jT kT Asymmetry in Longitudinally Polarized p+p Collisions at PHENIX - UVa - SPIN 2008

  4. Peripheral Collisions Larger Peripheral Collisions Larger Central Collisions Smaller Mechanism for . Same Helicity Measure jet Integrate over b, left with some residual kT kT Asymmetry in Longitudinally Polarized p+p Collisions at PHENIX - UVa - SPIN 2008

  5. Central Collisions Larger Peripheral Collisions Smaller Mechanism for . Opposite Helicity Integrate over b, left with some different residual kT kT Asymmetry in Longitudinally Polarized p+p Collisions at PHENIX - UVa - SPIN 2008

  6. Like Helicity kPR kTR Un-like Helicity kPR kTR Integrating over Impact Parameter Drell-Yan pair production in polarized p+p collisions. (Meng Ta-Chung et al. Phys. Rev. D 1989) Averaging over D(b): Integrating over impact parameter b: kT Asymmetry in Longitudinally Polarized p+p Collisions at PHENIX - UVa - SPIN 2008

  7. Measuring jet kT– di-hadron correlation Intra-jet pairs angular width : near jT Inter-jet pairs angular width : far jT ^ ^ pTa pTt • Zero kT pTa pTt jTy kT Asymmetry in Longitudinally Polarized p+p Collisions at PHENIX - UVa - SPIN 2008

  8. Measuring jet kT– di-hadron correlation Intra-jet pairs angular width : near jT Inter-jet pairs angular width : far jT  kT pTa pTt ^ ^ pTa pTt jTy • Zero kT • Non-Zero kT kTy kT Asymmetry in Longitudinally Polarized p+p Collisions at PHENIX - UVa - SPIN 2008

  9. Jet Kinematics pTa pTt ^ ^ pTa pTt pout jTy kTy pTt For details, see PRD 74, 072002 (2006) kT Asymmetry in Longitudinally Polarized p+p Collisions at PHENIX - UVa - SPIN 2008

  10. PHENIX Detector • Philosophy: • High resolution at the cost of acceptance • High rate capable DAQ • Excellent trigger capability for rare events • Central Arms: • ||<0.35, =2900 • Charged particle ID and tracking; photon ID. EM Calorimetry. • Muon Arm: 1.2<||<2.4 Muon ID and tracking. • Global Detectors • Collision trigger • Collision vertex characterization • Relative luminosity • Local Polarimetry kT Asymmetry in Longitudinally Polarized p+p Collisions at PHENIX - UVa - SPIN 2008

  11. Data Selection • Analyzed data sample from 2005 & 2006 RHIC Runs. • Integrated Luminosity: 2.5 pb-1 (Run 5) +6.4 pb-1 (Run 6) • Average beam polarization: 50% (Run 5), 57% (Run 6) • π° transverse momentum: 2 < pT < 10 GeV • h± transverse momentum: 2 < pT < 5 GeV • |η| < 0.35 kT Asymmetry in Longitudinally Polarized p+p Collisions at PHENIX - UVa - SPIN 2008

  12. π°Identificaton π°→γ+γ The pions are selected within Mπ◦ ±2.0σπ◦ Photon trigger: EMCal cluster energy > 1.4 GeV The mass, Mπ◦, and the width, σπ◦, are determined by fitting the di-photon mass spectrum with gaus+pol3. kT Asymmetry in Longitudinally Polarized p+p Collisions at PHENIX - UVa - SPIN 2008

  13. Correlation Function • Blue – real (raw Δφ) • Red – background (mixed events) kT Asymmetry in Longitudinally Polarized p+p Collisions at PHENIX - UVa - SPIN 2008

  14. Fit Function • Blue – real (raw Δφ) • Red – Fit from above equation kT Asymmetry in Longitudinally Polarized p+p Collisions at PHENIX - UVa - SPIN 2008

  15. kT results for unpolarized case kT = 2.88 +/- 0.02 (stat) +/- 0.12 (syst) GeV jT = 607.5 +/- 0.8 (stat) +/- 0.3 (syst) MeV kT Asymmetry in Longitudinally Polarized p+p Collisions at PHENIX - UVa - SPIN 2008

  16. Spin sorted dihadron correlations • Fit Results • Red – Like helicity (++ & --) • Blue – Unlike helicity (+- & -+) kT Asymmetry in Longitudinally Polarized p+p Collisions at PHENIX - UVa - SPIN 2008

  17. Need <zt> and xh <k2T> asymmetry results are not sensitive to this xh and <zt> values – only needed to set the scale. ^ ^ xh and <zt> are determined through a combined analysis of the π° inclusive cross section and using jet fragmentation function measured in e+e- collisions. Ref. PRD 74, 072002 (2006) kT Asymmetry in Longitudinally Polarized p+p Collisions at PHENIX - UVa - SPIN 2008

  18. Preliminary Results • Take the difference Like – Unlike helicities • Normalized by beam polarizations • <j2T > asymmetry small (-6 ± 6 MeV out of ~630 MeV for unpolarized) • <k2T > asymmetry also small (-8 ± 90 MeV out of ~2.8 GeV for unpolarized). kT Asymmetry in Longitudinally Polarized p+p Collisions at PHENIX - UVa - SPIN 2008

  19. Interpretation The small asymmetry in jT verifies our assumption that the third term is suppressed. The second term can be constrained from current knowledge of the π0 ALL. kT Asymmetry in Longitudinally Polarized p+p Collisions at PHENIX - UVa - SPIN 2008

  20. Interpretation The first term can be related in the “Meng conjecture” to partonic transverse momentum: where cij give the initial state weights and Wij give the impact parameter weighting. Since PYTHIA studies show that the final state studied here is dominated by gg scattering (~50%), We can interpret this as a constraint on the gluon orbital angular momentum. Consistent with previous (Sivers) measurements, and complimentary, since one naïvely needs no initial or final state interactions. kT Asymmetry in Longitudinally Polarized p+p Collisions at PHENIX - UVa - SPIN 2008

  21. Summary • We have an analysis tool – di-hadron azimuthal correlations - that allows us to measure kT. • We are studying this in helicity-sorted collisions to see if there is a spin-dependent, coherent component of kT. • In our kinematic range, we find jTRMS = -6 ± 6 MeV, and kTRMS = -8 ± 90 MeV. • While this is consistent with other measurements related to gluon OAM, the connection to parton OAM needs theoretical guidance! kT Asymmetry in Longitudinally Polarized p+p Collisions at PHENIX - UVa - SPIN 2008

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