Download - Douglas Fields University of New Mexico. Direct vs. Indirect Measurement Width of room Tape measure Spin ½ of proton Stern-Gerlach experiment ΔΣ DIS ΔG.

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Douglas Fields

University of New Mexico

Experimental Evidence for Partonic Orbital Angular

Momentum at RHIC

2Douglas Fields PacSPIN2011, Cairns, QLD, Australia

Direct vs. Indirect MeasurementWidth of room

Tape measureSpin ½ of proton

Stern-Gerlach experiment ΔΣ

DIS ΔG

DIS Q2 dependence, RHICBut, definition is unclear

Lg, Lq, Lg+q

Can one simply say L = ½ - ΔΣ - ΔG? No!Other methods…

Temperature of roomTape measure?

“Experimental Evidence”

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“Directly” measured quantity

Theory basis for implying indirect measurement

Limits on indirect measurement from experimental and theoretical uncertainties

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Template for Indirect Measurements

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RHIC Spin

BRAHMS & PP2PP (p)

STAR (p)

PHENIX (p)

AGS

LINACBOOSTER

Pol. Proton Source500 mA, 300 ms

%uptoPol

GeVs

70

50050

Spin Rotators

Partial Siberian Snake

Siberian Snakes

200 MeV Polarimeter AGS Internal PolarimeterRf Dipoles

RHIC pC PolarimetersAbsolute Polarimeter (H jet)

2 1011 Pol. Protons / Bunche = 20 p mm mrad

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Spin transport in Snake Magnets

Burkardt & Schnell Phys. Rev. D 74, 013002 (2006)Toy model for u-quarks in the valence region yields:

I.e., very weak (but nonzero) constraint on contributions of nonzero orbital angular momentum states to each quark flavor.

But the sum over flavors is not necessarily nonzero!

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Anomalous Magnetic Moment

5

1

91

5 Lx q x

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Single Spin Asymmetries (SSAs)

left

right

1 left rightN

left right

N NA

P N N

Fixed target pion SSAs (E704)

QCD prediction -> zero

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Early theoretical connection to OAM

There is a long history of trying to explain SSA’s with orbital motion. C.Boros, et al., PRL 70

p1751 (1993).Interaction with orbiting

valence quarks.

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More Modern Approach

Sivers Effect

Collins Effect

Sivers Function (angular momentum)

Transversity

(structure)

Collins Function (Fragmentation)

1 1 1

1 ...left right

N T

left right

N NA f D δq H

P N N

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• Nice conceptual picture from D. Sivers (talk given at UNM/RBRC Workshop on Parton Orbital Angular Momentum).

• Summary:– Sivers effect

requires orbital motion.

– Is process dependent.

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How can you get a net kT?

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Relation to GPDs• Leads to Asymmetric

parton densities.• Which leads to

preferential left-right interaction depending upon direction of OAM relative to spin direction.

• Which leads to left-right scattering depending upon the initial/final state interactions.

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Effect requires OAM

• So what do we see at RHIC?

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Neutral meson SSAs (STAR forward)

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Neutral meson SSAs (PHENIX forward)

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xF scaling

Larger asymmetries at larger xF

Valence quark effects?

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Combined π0 forward

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Charged mesons in muon arms.

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Charged meson SSAs (PHENIX forward)

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Charged meson SSAs (BRAHMS forward)

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Combined charged meson SSAs (forward)

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Seen as a limit on Gluon Sivers

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Charged/neutral meson SSAs (PHENIX central)

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Sivers functionsHave extracted Siver’s

functions for DIS.Can extend to include

RHIC data?What does it mean for

OAM?

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p+p and p+C CNI Asymmetry

Prelim

inar

yRer5=0, Imr5=0no hadron spin-flip

p+p CNI (jet) p+C CNI

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Some (rather old) theoretical connection…

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Forward Neutron SSA~ 1800cm

10cm±3 mradDx magnetblue beam yellow beam

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Forward Neutron SSAInclusive neutron

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OPE fails to predict both the cross section and the asymmetry.

Also possible relation to OAM?

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Model prediction

B.Z. Kopeliovich et al.arXiv: 0807:1449

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Jet SSAs (STAR)

Boer & Vogelsang, PRD 69 (2004) 094025

jet

jet

AN pbeam (kT ST)

pbeam into page

Idea: directly measure kT by observing momentum imbalance of a pair of jets produced in p+p collision and attempt to measure if kT is correlated with incoming proton spin

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What is the origin of jet 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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Origin of Jet kT

Di-hadron pT

kT

Net transverse momentum of a di-hadron pair in a factorization ansatz

• I = initial – fermi motion of the confined partons, initial-state gluon radiation… • S = soft – one or several soft gluons emitted• H = hard – final-state radiation (three-jet)…

Another Possibility:Spin-correlated transverse momentum – partonic

orbital angular momentumCan examine the helicity dependence of each term:

2

2

2

0?

0

0?

T initial

T soft

T hard

k

k

k

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Peripheral Collisions

Larger

Jet 1

Jet 2 w/<kT>=0

Jet 2

Integrate over b, leftwith some residual kT

2Tk

Net pT kick

Central Collisions

Smaller 2TkJet 2

Jet 1

Jet 2 w/<kT>=0

Like helicities: Beam momenta

Partonic orbital angular momentum leads to rotation of partons correlated with the proton spin vector

This leads to different pT imbalances (pT-kicks) of jet pairs in semiclassical models

Can be measured by measuring helicity dependence of <kT

2>

For details on jets see: Phys. Rev. D 74, 072002 (2006)

kT Asymmetry

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Partonic orbital angular momentum leads to rotation of partons correlated with the proton spin vector

This leads to different pT imbalances (pT-kicks) of jet pairs in semiclassical models

Can be measured by measuring helicity dependence of <kT

2>

Integrate over b, leftwith different residual kT

Net pT kick

Central Collisions

Larger 2TkJet 2

Jet 1

Jet 2 w/<kT>=0

2Tk

Peripheral Collisions

Smaller Jet 1

Jet 2 w/<kT>=0

Jet 2

Unlike helicities: Beam momenta

For details see: Phys. Rev. D 74, 072002 (2006)

kT Asymmetry

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Integrating over Impact Parameter

Drell-Yan pair production in polarized p+p collisions.(Meng Ta-Chung et al. Phys. Rev. D 1989)

kPR

kTR

kPR

Like Helicity

Un-like Helicity

kTR),(),()( 222 bpbpbp ttt

TPTRPRTRPRTPt kkkkbp cos);,,(22

2

Averaging over D(b):

Integrating over impact parameter b:

TRPRR

Rt

kkk

kp

22 9.1

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Measuring jet kT – di-hadron correlationIntra-jet pairs angular width : near jT

Inter-jet pairs angular width : far jT j Typ Tt

p Ta

p Ta^

p Tt^• Zero kT

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Measuring jet kT – di-hadron correlation

• Non-Zero kT

kT

Intra-jet pairs angular width : near jT

Inter-jet pairs angular width : far jT j Typ Tt

p Tap Ta^

p Tt^

k Ty

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Jet Kinematics

Tt

Ttt p

pz

ˆ

j Typ Tt

p Tap Ta^

p Tt^

k Ty

p Ttp out

For details, see PRD 74, 072002 (2006)

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Measuring jet kT – di-hadron correlationo- h± azimuthal correlation

Trigger on a particle, e.g. o, with transverse momentum pTt. Measure azimuthal angular distribution w.r.t. the azimuth of associated (charged) particle with transverse momentum pTa. The strong same and away side peaks in p-p collisions indicate di-jet origin from hard scattering partons.

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Both jT and kT consistent with zero.

We now have higher statistics data which we will soon analyze.

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PHENIX Results

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The first term can be related in the “Meng conjecture” to partonic transverse momentum:

where cij give the initial state weights and Wij give the impact parameter weighting.

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Interpretation

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Relating to Meng…

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Since PYTHIA studies show that the final state studied here is dominated by gg scattering (~50%),

We can interpret this as a (rather weak) constraint on the gluon orbital angular momentum.

Consistent with previous (Sivers) measurements, and complimentary, since one naïvely needs no initial or final state interactions (although Sivers measures orbital in transversely polarized proton).

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Interpretation

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We have an analysis tool – di-hadron azimuthal correlations - that allows us to measure kT.

We are studying this in helicity-sorted collisions to see if there is a spin-dependent, coherent component of kT.

In our kinematic range, we find jT RMS = -3 ± 8(stat) ± 5(syst) MeV, and kT RMS = -37 ± 88 ± 14(syst) MeV.

While this is consistent with other measurements related to gluon OAM, the connection to parton OAM needs theoretical guidance!

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kT Asymmetry Summary

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Drell Yan:

Plans to look at intermediate mass range.Is that

sufficient?

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Future

ϒ-states

J/Ψ

Drell Yan

Ψ’

charm

bottom

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For the non-zero DIS result, Q2=1GeV.

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Drell Yan

0.1 0.2 0.3 x

Siv

ers

Am

plit

ude

0

HERMES Sivers Results

Markus DiefenthalerDIS WorkshopMűnchen, April 2007

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There are many direct measurements that have been/will be made at RHIC that have a connection to Partonic Orbital Angular Momentum.

Theoretical work is needed to relate these measurements to OAM on a more quantitative footing.

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Summary

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Backups

Fit Function

• Blue – real (raw Δφ)• Red – Fit from above

equation

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2

22

22

2/3

2/

2/3

2/

21

2

sinexp

/22

cos

)0(1

out

Ta

outTaout

Taaway

awayo

mixreal

p

p

ppErfp

p

d

dN

d

dNCGausCC

d

dN

Nd

dN

Need <zt> and xh

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<k2T> asymmetry results are

not sensitive to this xh and <zt> values – only needed to set the scale.

^

xh and <zt> are determined through a combined analysis of the π° inclusive cross section and using jet fragmentation function measured in e+e- collisions. Ref. PRD 74, 072002 (2006)

^

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kT results for unpolarized case