Finding The Spin of the Proton Douglas Fields University of New Mexico.

Finding The Spin of the Proton

Douglas FieldsUniversity of New Mexico

February 4, 2009 LANL P-25 Seminar 2

Outline

• Review of Problem– Brief Review of Deep Inelastic Scattering– Spin “Crisis”

• Spin physics at RHIC– RHIC and PHENIX– Measurements of ΔG– “Measurements” of ΔL

• PHENIX upgrades and future measurements


Motivation

• Hadron Physics:– Understanding of the structure of the nucleon.– Understanding of nuclear interactions.– Tests of QCD.

• Standard Model Tests:– Use spin as a tool to test Standard Model

predictions.– Search for exotics (SUSY, PV…).

• Forget all of that– Spin is as fundamental as charge or mass!


Spin Effects

•Polarized pp elastic scattering at 197MeV.

•Ay ~ (NL – NR)/ (NL + NR)

•Shows that the strong (nuclear) force depends strongly on the spin orientation.

p

p

NL

NR


“Naïve Quark Model”• Protons are spin ½

objects composed of three spin ½ objects.

u

d

u

duuuuduududuudu

duuuudduuuduP222

18

1

singlet.color

only ric,Antisymmet symmetric. bemust Product symmetric. momentum,

angular noWith

)color()flavor()spin()space(

Since Quarks are fermions, total wavefunction must be antisymmetric


Strong Spin Dependence• Deltas are spin

3/2 objects composed of three spin ½ objects.

• Mass is ~300MeV greater than proton!

u

d

u

uudduuudu

P 3

1


Predictions• Baryon magnetic moments are

well predicted by the Naïve Quark Model

mu = md ~ 1/3mp

ms given by magnetic moment(but mu=4MeV, md=7MeV)?

q

qq m

Q

2


Caveat…• Quarks (and anti-quarks) only account

for ½ of nucleon momentum and it is dependent on at what scale you observe.•I like the fractal analogy:

•At low resolving power, one sees three quarks in the nucleon

•At higher resolving power, one sees more and more detail of what a quark is, namely a collection of quarks, antiquarks and gluons.

Resolving power (smaller scales)


What Does the Proton Look Like?• The distribution of partons in the

proton was not very well understood 10 years ago

• Today, the picture is different…

J.D. Bjorken, Collisions Of Constituent Quarks At Collider Energies SLAC-PUB-95-6949 (1995)


Probing the Proton• EM interaction

– Photon• Sensitive to electric charge2

• Insensitive to color charge

• Strong interaction– Gluon

• Sensitive to color charge• Insensitive to flavor

• Weak interaction– Weak Boson

• Sensitive to weak charge ~ flavor• Insensitive to color


• Longitudinal momentum fraction (x)• Transverse position (b)

• Intrinsic transverse momentum (kT)

• Correlations of above (x┴ x kT)

Missing Ingredients

P.H. Hägler, et. al.


Parton Distribution Functions• Quark Distributions

q(x,Q2)=

q(x,Q2)=

q(x,Q2)=

=

unpolarized distributionunpolarized distribution

helicity distributionhelicity distribution

transversity distributiontransversity distribution

g(x,Q2)=

g(x,Q2)=

No Transverse Gluon Distribution in 1/2

• Gluon Distributions


Sum Rules

• Momentum Sum Rule• Helicity Sum Rule:

• ΔΣ measured in DIS experiments and found to be small (0.1 – 0.3)…

q

q

G

1 1s = = +L

2 2 = u + d + s =

L

L

G =

GL G

polarization of quarks and antiquarks

polarization of quark orbital angular momentum

polarization of gluon orbital angular momentum

polarization of

, u u u .

gluons

where etc

1

0

1xq x xg x dx


“Spin Crisis”

05.027.0

12.060.0

123)(18 2

22

1

0

p1

QDFdxxg S

s

• “Not-so-Naïve” quark model and comparison to results

Predicted from EJSR

Measured in DIS


Not Really a Crisis…• Remember the more complicated

possibilities…

• But Leptons don’t scatter off gluons (at first order)

• How do we probe the gluons?

GLG qL+ 2

1 =

2

1 = s

G GG


RHIC Spin

BRAHMS & PP2PP

STAR

AGS

LINACBOOSTER

Pol. H- Source

Spin Rotators(longitudinal polarization)

Solenoid Partial Siberian Snake

Siberian Snakes

200 MeV Polarimeter AGS Internal Polarimeter

Rf Dipole

RHIC pC PolarimetersAbsolute Polarimeter (H jet)

AGS pC PolarimetersStrong AGS Snake

Helical Partial Siberian Snake

PHOBOS

Spin Rotators(longitudinal polarization)

Spin flipper

Siberian Snakes

PHENIX

PHENIX Detector

•Central Arms:||<0.35, =2900

Charged particle ID and tracking; photon ID. EM Calorimetry.Muon Arm:1.2<||<2.4Muon ID and tracking.

•Global DetectorsCollision triggerCollision vertex characterizationRelative luminosityLocal Polarimetry

•Philosophy:– High resolution at the cost of acceptance– High rate capable DAQ– Excellent trigger capability for rare events



“Measurements” of ΔG• Example:

– choose channel with high statistics– p + p → π0 + X– Complicated mixture of amplitudes– Compare with:

gqgq G

G

q

q

qqqqq

q

q

q

gggg G

G

G

G

1

expLLY B

N N N NA

P P N N N N


Solution• Factorization between hard and soft physics

– Example: q + g → π0 + X

Dp

p

Hard Physicsσ ~ momenta and helicities

• Soft:– q(x), Δq(x), D(z)

• Hard:– NLO pQCD cross-

sections – spin dependent

• Missing ingredients: – Δg(x)– beam polarization

Soft Physicsfrom universalfits to data


Status of Ingredients

• Status of Pol. PDFs (2004)

• Valence quark fairly well determined from DIS

• ΔG and sea quarks poorly known


pQCD Check• Next step: Measure

cross-section as a test for perturbative QCD at

• Run 6, pushes 0 cross-section to 20 GeV/c.

• Agreement with pQCD over broad range of pT.

• Does this mean that QCD works for spin sorted in this same range?

.200GeVs

pp0 X : PRD76,051106


Where Are We So Far?• Factorization between hard and soft physics

– Example: q + g → π0 + X

Dp

p

Hard Physicsσ ~ momenta and helicities

• Soft:– q(x), Δq(x), D(z)

• Hard:– NLO pQCD cross-

sections – spin dependent

• Missing ingredients: – Δg(x), P – beam

polarization

Soft Physicsfrom universalfits to data

☺ ☺ ☺

☺

☺


π0 ALL

• Put all ingredients into a NLO pQCD calculation with assumed values of ΔG, Monte Carlo the results with the detector acceptance, and compare to data to determine allowed values of ΔG.

arXiv:0810.0694

From ALL to G (with GRSV model)


arXiv:0810.0694

Compare ALL data to curves (produce 2 vs G)

1.0:error.expSyst. )3(2.0and)1(1.02.04:errorStat. 2.0

8.022]3.0,02.0[

GeVG x

GRSV

Generate g(x) curves for different (with DIS refit)

1

0)( dxxgG

Calculate ALL for each G


Update to Pol. PDFs

• Using the π0 results from PHENIX, one can recalculate allowed values of the pol. PDFs.

• Much improved limits on ΔG.


ΔL

• ΔG is appearing to be small (although it may be enough to solve the Spin Crisis)

• What is next?• ΔL…• Theory tells us it should be there

anyway.– Anomalous magnetic moment– Sivers Effect

q

1 1s = = +L

2 2 GL G


Sivers Effect

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).SP

kT,qp

p

FSI : SIDISISI : Drell-Yan


How can you get a net kT?

• 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.

• I would like to just follow this conceptual picture to see where it may lead.


Sivers Effect

No Sivers Effectwithout interactionwith absorber.


Fields Effect• Think of rotating (longitudinal) water balloons,

or…

Origin of Jet kT

Another Possibility:• Spin-correlated transverse momentum – partonic

orbital angular momentum• Can examine the helicity dependence of each term:

Di-hadron pT

kT


2 2 2 2T T T Tdi hadron initial hard frag

k k k k

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

• initial – e.g., fermi motion of the confined quarks or gluons, initial-state gluon radiation…

• hard – final-state radiation (three-jet)…• frag – fragmentation transverse momentum jT

2

2

2

0

0

1

T initial

T hard

T frag

k

k

kQ


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


Un-like Helicity(Positive On Negative Helicity)

Peripheral Collisions

Smaller

Central Collisions

Larger

Integrate over b, leftwith some differentresidual kT

2Tk

2Tk

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

kTRkPR

kTR

kPR

Like Helicity

Un-like Helicity

),(),()( 222 bpbpbp ttt

TPTRPRTRPRTPt kkkkbp cos);,,(22

2

Averaging over D(b):

Integrating over impact parameter b:

TRPRR

Rt

kkk

kp

22 9.1


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.


How does PHENIX measure kt?

• Zero kT

• Non-Zero kT

Intra-jet pairs angular width : near jT

Inter-jet pairs angular width : far jT kT

Drawings by A. Zimmerman

near

far


Jet Kinematics

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


Correlation Function• Red – real (raw Δφ)• Blue – background (mixed events)

Fit Function

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

equation


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

Spin sorted dihadron correlations

Fit Results• Red – Like helicity (++ & --)• Blue – Unlike helicity (+- & -+)


Need <zt> and xh


<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)

^

kT results for unpolarized case


jT = 607.5 +/- 0.8 (stat) +/- 0.3 (syst) MeV

kT = 2.88 +/- 0.02 (stat) +/- 0.12 (syst) GeV

Preliminary Results

• Take the difference Like – Unlike helicities.

• Normalized by beam polarizations.

• <j2T > asymmetry small (-6 ± 6 MeV out of ~607 MeV for unpolarized).

• <k2T > asymmetry also

small (-8 ± 90 MeV out of ~2.9 GeV for unpolarized).


• The small asymmetry in jT verifies our assumption that the third term is suppressed.

• The second term may be constrained from current knowledge of the π0 ALL.

Interpretation


2

2

2

0

0

1

T initial

T hard

T frag

k

k

kQ

• 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.

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

• We can interpret this as a constraint on the gluon orbital angular momentum.

• Consistent with previous (Sivers) measurements, and complimentary, since one naïvely needs no initial or final state interactions.

Interpretation


2 ij ij i j i jT T T T Tinitial

i j

k c W k k k k


What Next?


PHENIX VTX Detector Upgrade

• Main physics goal to discriminate heavy-flavor production via displaced vertices.

• I would like to use it to better determine jet kT.

• Needs simulation and study.

Summary

• 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 = -6 ± 6 MeV, and kT RMS = -8 ± 90 MeV.

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



Summary

• Our group has made significant contributions to the RHIC Spin program and to the PHENIX experiment.

• We are currently leading the investigation of an interesting, albeit speculative, physics analysis.

• We will continue significant contributions to the PHENIX upgrade plan with an eye on our research thrust.

• I look forward to an invigorated nuclear/particle group with the addition of active theorists.

Backups



How do you measure the quark spins?

k k/

X

q

~ l-q elastic scattering

Leading order diagram.

+ Radiative corrections

+ NLO corrections

+ Higher twist…


eμ Elastic Scattering

e-(p1,s1)

e-(p2,s2)

-(p3,s3)

-(p4,s4)

),( q

Initial State Potential Final State

Probability to happen:

2State InitialPotentialState Final


Feynman Prescription…

2k

gi

),( 44 spu

),( 33 spu

ie

),( 11 spu

ie

),( 22 spu

EM coupling strength e

EM coupling strength e

M

Q

M

Q

kkkddQ

d

22sin22cos

1

2sin4

22

2

22

42

2

2

2

Electric interaction

Magnetic interaction

2sin22cos1

2sin42

12

242

2

2

2

WWkkkddQ

d


Now, for e-quark scattering• eq scattering

• Now, assume:

• So that,

iiii

i

m

Q

m

Qee

kkkddQ

d

22sin242cos

1

2sin4

22

2

2222

42

2

2

2

Modified by the quark fractional

chargeModified by the

quark mass

xMmxpp ii and,

MxQeW

MxQ

xM

QeW

ii

ii

2

242

22

2

22

22

1


Step towards protons…• Sum over quark flavors and integrate

over x weighted by f(x), the probability to have momentum fraction x:

)(),(

)()(),(

2)(

12

1

222

2

1

0

22

2

xFQMW

xFxxfeQW

MxQexdxfW

iii

ii

•Electric STRUCTURE Function

•Magnetic STRUCTURE Function


Structure Functions

MQx

where

xgqGM

xgqGM

xFqW

xFq

2

,

)(),(

)(),(

)(),(

)(),(MW

then,fixed, ratio with their

large become and Q when limit, scalingBjorken In the

2

22

22

12

12

22

2

12

1

2

• Structure functions in the scaling limit

Spin independent

Spin dependent (= 0 when sum over spins)

This is related to the elastic scattering off parton with momentum fraction p = xP


Nosecone Calorimeter

Tungsten absorber

Pb absorber

Pad readoutStripixel readout

Cu skin

15 m

m

15 m

m

• Main physics goals to measure γ-jet events and isolate muons from W-decay

• I would like to use it to better determine jet kT.

• Needs simulation and study.

Finding The Spin of the Proton Douglas Fields University of New Mexico.

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