6/2/2005douglas fields1 measuring orbital angular momentum through jet k t douglas fields university...
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6/2/2005 Douglas Fields 1
Measuring Orbital Angular Momentum through Jet kT
Douglas Fields
University of New Mexico/RBRCJan Rak, Rob Hobbs, Imran Younus
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• 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.,
Basic Picture
Positive Helicity
Positive Helicity
Positive Helicity
Negative Helicity
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Like Helicity(Positive on Positive Helicity)
Central Collisions
Smaller
Peripheral Collisions
Larger
Integrate over b, leftwith some residual kT
Measure jet 2Tk
Peripheral Collisions
Larger
2Tk
2Tk
2Tk
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Un-like Helicity(Positive On Negative Helicity)
Peripheral Collisions
Smaller
Central Collisions
Larger
Integrate over b, leftwith some differentresidual kT
2Tk
2Tk
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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)
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.
Total transverse momentum squared of partons
kTRkPR
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From Meng Ta-Chung et al.Phys Rev. D40, p769, (1989)
The constant terms in pt cancel and we have
We can now helicity separate:b
We can then average over the impact parameter
kTRkPR
kTR
kPR
Like Helicity
Un-like Helicity
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From Meng Ta-Chung et al.Phys Rev. D40, p769, (1989)
This paper makes the following assumptions:1) Uniform spherical density F(b,θP,θT)2) kPR~kTR~kR (no dependence on b, θP, θT.)
Then,
Evaluated numerically
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How Large an Effect Can We Expect?
1 0.2
1 200 per unit of
0.5 400 per unit of
zL GeV fm r p
r fm p MeV
r fm p MeV
20.01T
T
px p
s
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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?
Intra-jet pairs angular width : N jT
Inter-jet pairs angular width : A jT kT
0 - h azimuthal correlation functions
Trigger 0
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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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π0 Identification
• PHENIX has central arm EMCal with electron rejection in RICH.
• Used shower profile cut.
• Good S/B at higher pt (>2GeV).
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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 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 3.0<pT<4.0
Fit = const + Gauss(0)+Gauss()
real mixedij ij
ijij ij
dN dNC ( ) /
d dnorm
1.5<pT<2.0
Intra-jet pairs angular width : N jT
Inter-jet pairs angular width : A jT kT
mixed realN N
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Jet Kinematics
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How accurately can we measure <kt>?
• is extracted from and fragmentation functions which are extracted from the inclusive distributions.
2Tk
2Tj
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How accurately can we measure Δ<kt>?
• ZT uncertainties should cancel in the difference• Bunch Shuffling in Run3 (PHENIX)
– δ Δ<kt> ~ 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 (PY*PB) than Run3
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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…