Measuring Orbital Angular Momentum through Jet k T

6/20/2005 Douglas Fields RHIC-AGS User's Meeting

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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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Outline

• Spin dependent jet kT

– Sivers function– Question…– Something new

• How does PHENIX measure jet kT?– Correlation functions– PHENIX detector

• Origin of jet kT

• Summary


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What is the origin of kT?

Intrinsic (Confinement) kT 200 MeV/c

Breaks collinear factorization

Soft QCD radiation.

An example - J/ production.

Extra gluon kick

pTJ/ =1.80.230.16 GeV/c

Phys. Rev. Lett. 92, 051802, (2004).


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Another Possibility

• Spin-Correlated transverse momentum – Partonic orbital angular momentum

• We can perhaps measure using jet kT

– Sivers Effect in single (double?) transverse spin

– Possible Effect in double longitudinal spin


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Sivers Fcn from Back2Back AnalysisBoer and Vogelsang, Phys.Rev.D69:094025,2004, hep-ph/0312320

TT

TTT

NTTT kPS

kPSkxfkxfSkxf

)(),(

2

1),(),,(

•Non-Zero Sivers function means that there is a left/right asymmetry in the kT of the partons in the nucleon

•For a positive Siver’s function, there will be net parton kT to the left (relative to direction of proton, assuming spin direction is up).

•Boer and Vogelsang find that this parton asymmetry will lead to an asymmetry in the distribution of back-to-back jets

•There should be more jets to the left (as in picture to the left).•Should also be able to see this effect with fragments of jets, and not just with fully reconstructed jets?

•Take some jet trigger particle along ST axis (either aligned or anti-aligned to ST)•Trigger doesn’t have to be a leading particle, but does have to be a good jet proxy•Then look at distribution of away side particles

See talk

tomorrow ??


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Sivers Effect

• Recently, at the RBRC Single Spin Workshop, Denis Sivers gave a nice conceptual (no twist-anything) picture of how orbital angular momentum could cause a single transverse spin asymmetry.– “Quantum Fan” description (top view – spin down):

No Sivers Effectwithout interactionwith absorber – Higher twist effect


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Sivers Effect• Night before last, I was thinking…

– Why not double spin?


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• Idea came from me trying to understand Sivers effect.– I basically got the picture wrong – I couldn’t understand how single

transverse spin effects could cause an asymmetry – so I started playing around with double longitudinal spin asymmetries.

• Same idea of rotating partons around spin direction• Two classes of collisions:

– Like helicity, i.e.,

– Un-like helicity, i.e.,

Similar Idea for “Fields” Effect

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 jetPeripheral 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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“Fields” Function

• Something like:

kTRkPR

ˆ ˆ ˆ ˆT T T P P PS b k S b k bT bP


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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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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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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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Our Model

• We first assume constant angular velocity of partons, pθ, regardless of distance to the proton center.

• We set (arbitrarily) the maximum transverse momentum of the partons to be 300 Mev at the radius of the proton equal to 1.3 fm.


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Our Model

• Use different transverse density distributions to get pt kick from coherent spin-dependent motion:


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Our Model Results

• Basically independent of transverse density distribution.

• Ranges from 0.3 to 0.6 times the initial momentum.

• Very crude – would like suggestions to improve.


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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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Centrality Dependence

• 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 does PHENIX 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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jetˆTp

Tp

*

kT, jT “easy” measurement in p +p

*cos( )ˆ

T

T

pz

p

*ˆ sin( )T Tj p fragmentation

near

far

jT N

jet fragmentation transverse momentum, jT-scaling.

kT 2F-2

N

parton transverse momentum, intrinsic + NLO radiative corrections.


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Jet Kinematics


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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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How accurately can we measure <kt>?

• is extracted from , σF, and fragmentation functions (to get zt) which are extracted from inclusive and associated distributions.

2Tk

2Tj


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Origin of kT

Breaks collinear factorization

An example - J/ production.

pTJ/ =1.80.230.16 GeV/c

Phys. Rev. Lett. 92, 051802, (2004).

2 2 2

intrinsic soft O

2 2

NL

1

2T Tpair T T Tk k kp k


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Hard Scattering kT

• acoplanar in PL PT space

• collinear in PX PY space

transverse

Longitudinal

jet

jet

• acoplanar in PL PT space

• acoplanar in PX PY space

transverse

Longitudinal


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Spin Sorted Analysis• Do exactly the same analysis sorted on same

and opposite helicity bunch crossings, extract <zkt>RMS and look at the difference.

Δφ Δφ

C(Δ

φ)

C(Δ

φ)

Same Helicity Opposite Helicity


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Run03 Data

trigger π0

1< pTt<3 Gev/c

3<pTt<7 Gev/c

Associated h

1< pTa<2.5 Gev/c

Like sign

Unlike sign


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Systematic Check

• Helicity assignments are randomized, and then the kT difference calculated for each randomized set.

• The width of the distribution for all the randomized sets should be the same as our statistical errors on the previous plot.

RMS = 45

RMS = 90


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Run03 DataIts too early to make a definite statement about the apparent excess as the systematic uncertainties are being evaluated.

However, there is an ongoing analysis of 10x more stat. and 2x better polarization in run05 should yield a definite answer.

BS variance


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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

• Jet kT can be extracted from di-hadron correlations using method developed by J. Rak and others.

• Jet kT can be used to probe initial and final state contributions to transverse momentum distributions.

• We can make a measurement of the spin dependence of jet <kT> in:– Single transverse spin asymmetries – Sivers Function.– Double-longitudinal spin asymmetry – Fields Function.

• These may be sensitive to orbital angular momentum.• Need theoretical guidance…

Documents

Measuring Orbital Angular Momentum through Jet k T