Measuring Orbital Angular Momentum through Jet kT

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Measuring Orbital Angular Momentum through Jet kT

• Douglas Fields
• University of New Mexico/RBRC

Jan Rak, Rob Hobbs, Imran Younus
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Basic Picture

• Idea came from me trying to understand Sivers
  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.,

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Like Helicity(Positive on Positive Helicity)
Measure jet
Integrate over b, left with some residual kT
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Un-like Helicity(Positive On Negative Helicity)
Integrate over b, left with some
different residual kT
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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

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From Meng Ta-Chung et al.Phys Rev. D40, p769,
(1989)
kTR
kPR
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From Meng Ta-Chung et al.Phys Rev. D40, p769,
(1989)
Like Helicity
kTR
kPR
Un-like Helicity
kPR
kTR
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From Meng Ta-Chung et al.Phys Rev. D40, p769,
(1989)

• This paper makes the following assumptions
• Uniform spherical density F(b,?P,?T)
• kPRkTRkR (no dependence on b, ?P, ?T.)
• Then,

Evaluated numerically
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How Large an Effect Can We Expect?
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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.

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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?
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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

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p0 Identification

• PHENIX has central arm EMCal with electron
  rejection in RICH.
• Used shower profile cut.
• Good S/B at higher pt (gt2GeV).

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Charged Particles

• Tracks in the Drift Chamber
• Hits in the Pad Chambers
• RICH veto for low momentum
• Shower shape cut at high momentum

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Correlation Functions

• dNreal ?f distribution from particles in the
  same event
• dNmixed ?f distribution from particles in
  different events with similar vertex position
• Norm
• Fit to two gaussians plus a constant term

1.5ltpTlt2.0
Fit const Gauss(0)Gauss(??)
3.0ltpTlt4.0
Intra-jet pairs angular width ?N ? ?jT?
Inter-jet pairs angular width ?A ? ?jT? ? ?kT?
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Jet Kinematics
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How accurately can we measure ltktgt?

• is extracted from and
  fragmentation functions which are extracted from
  the inclusive distributions.

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How accurately can we measure ?ltktgt?

• ZT uncertainties should cancel in the difference
• Bunch Shuffling in Run3 (PHENIX)
• d ?ltktgt 80MeV

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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 (PYPB) than Run3

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Summary

• We can make a measurement of the
  double-longitudinal spin dependence of jet ltkTgt.
• 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