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Measuring Orbital Angular Momentum through Jet k T

Measuring Orbital Angular Momentum through Jet k T. Douglas Fields University of New Mexico/RBRC. Jan Rak, Rob Hobbs, Imran Younus. Positive Helicity. Positive Helicity. Positive Helicity. Negative Helicity. Basic Picture. Idea came from me trying to understand Siver’s effect

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Measuring Orbital Angular Momentum through Jet k T

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  1. Measuring Orbital Angular Momentum through Jet kT Douglas Fields University of New Mexico/RBRC Jan Rak, Rob Hobbs, Imran Younus Douglas Fields

  2. Positive Helicity Positive Helicity Positive Helicity Negative Helicity Basic Picture • Idea came from me trying to understand Siver’s effect • Quantum Fan Level Description • This is a double spin asymmetry • This is for longitudinally polarized protons • Rotating partons around spin direction • Two classes of collisions: • Like helicity, i.e., • Un-like helicity, i.e., Douglas Fields

  3. Peripheral Collisions Larger Peripheral Collisions Larger Central Collisions Smaller Like Helicity(Positive on Positive Helicity) Measure jet Integrate over b, left with some residual kT Douglas Fields

  4. Central Collisions Larger Peripheral Collisions Smaller Un-like Helicity(Positive On Negative Helicity) Integrate over b, left with some different residual kT Douglas Fields

  5. History • Talked to many people – Werner pointed me to a paper by Meng Ta-chung et al. • “Experiment B” – similar idea, only for Drell-Yan Douglas Fields

  6. Total transverse momentum squared of partons For a particular impact parameter, b, the average transverse momentum Where, is the product of the Jacobian and the density profile of partons, and D(b) is the overlap region. From Meng Ta-Chung et al.Phys Rev. D40, p769, (1989) kPR kTR Douglas Fields

  7. b The constant terms in pt cancel and we have We can now helicity separate: We can then average over the impact parameter From Meng Ta-Chung et al.Phys Rev. D40, p769, (1989) Like Helicity kPR kTR Un-like Helicity kPR kTR Douglas Fields

  8. From Meng Ta-Chung et al.Phys Rev. D40, p769, (1989) • This paper makes the following assumptions: • Uniform spherical density F(b,θP,θT) • kPR~kTR~kR (no dependence on b, θP, θT.) • Then, Evaluated numerically Douglas Fields

  9. How Large an Effect Can We Expect? Douglas Fields

  10. Pause For Feedback • Need theoretical guidance! • Would be nice to have experimental handle on impact parameter: • Multiplicity • Forward or central • Underlying event… • but, not explicitly necessary. Douglas Fields

  11. How do we measure kt? • 0 - h azimuthal correlation functions Trigger0 Intra-jet pairs angular width : N jT Inter-jet pairs angular width : A jT  kT Douglas Fields

  12. PHENIXDetector Overview • East Arm • tracking: • DC, PC1, TEC, PC3 • electron & hadron ID: • RICH,TEC/TRD, • TOF, EMCal • photons: • EMCal • West Arm • tracking: • DC,PC1, PC2, PC3 • electron ID: • RICH, • EMCal • photons: • EMCal Douglas Fields

  13. π0 Identification • PHENIX has central arm EMCal with electron rejection in RICH. • Used shower profile cut. • Good S/B at higher pt (>2GeV). Douglas Fields

  14. Charged Particles • Tracks in the Drift Chamber • Hits in the Pad Chambers • RICH veto for low momentum • Shower shape cut at high momentum Douglas Fields

  15. Correlation Functions • dNreal Δφ distribution from particles in the same event • dNmixed Δφ distribution from particles in different events with similar vertex position • Norm = • Fit to two gaussians plus a constant term 1.5<pT<2.0 Fit = const + Gauss(0)+Gauss() 3.0<pT<4.0 Intra-jet pairs angular width : N jT Inter-jet pairs angular width : A jT  kT Douglas Fields

  16. Jet Kinematics Douglas Fields

  17. How accurately can we measure <kt>? • is extracted from and fragmentation functions which are extracted from the inclusive distributions. Douglas Fields

  18. How accurately can we measure Δ<kt>? • ZT uncertainties should cancel in the difference • Bunch Shuffling in Run3 (PHENIX) • δ Δ<kt> ~ 80MeV Douglas Fields

  19. For Run5 • ~10-20 times more statistics than Run3 • Statistical errors smaller by factor of 3-5 • Polarization in Run5 ~55% • Effect larger by factor of ~5 (PY*PB) than Run3 Douglas Fields

  20. Summary • We can make a measurement of the double-longitudinal spin dependence of jet <kT>. • This may be sensitive to orbital angular momentum. • These effects (if really there) may also influence the double-longitudinal cross-section asymmetry. • Need theoretical guidance… Douglas Fields

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