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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…