UMass Amherst Christine A. Aidala The Whole Story Behind a Half: The Quest to Understand the Proton’s Spin Sambamurti Memorial Lecture BNL July 22, 2008

UMass AmherstChristine A. Aidala

The Whole Story Behind a Half:

The Quest to Understand the Proton’s Spin

Sambamurti Memorial LectureBNL

July 22, 2008

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Christine Aidala, Sambamurti Lecture, 7/22/2008

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What is Spin?Spin is a quantum mechanical property of fundamental particles or combinations of particles.

It’s called “spin” because it’s a type of angular momentum and is described by equations treating angular momentum.

?

In a magnetic field, different spin states split into different energy levels.

The units of angular momentum are the same as Planck's constant, h and can only have values that are integer : 0, 1, 2, 3, . . . or half-integer: 1/2, 3/2, 5/2, . . .

Proton spin is what makes MRI possible!


32s+1 Energy Levels

Any particle with spin

0

z

Β

Spin ½ particle (e.g. 107Ag or 1H)

0

z

Β

Spin 1 particle (e.g. 2H)

0

z

Β

Spin 3/2 particle (e.g. 7Li)

0

z

Β

Stern-Gerlach ExperimentA

pply a magnetic field


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Looking Inside the Proton:The Quark-Parton Model

• Similarly to Rutherford’s 1911 experiment in which the scattering of alpha particles at large angles off of gold revealed a hard atomic core (the nucleus), in the late 1960’s at SLAC, scattering of electrons at large angles off of protons revealed “hard” subcomponents in the proton – Protons weren’t solid lumps of positive

charge as previously believed!

– The pointlike constituents that make up the proton are called “quarks,” or slightly more generally, “partons.” Quark

Quarks, like protons, have spin 1/2.


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Quark-Parton Model (cont.)

• But these quarks are not completely free in the nucleon!– Bound by force-carrier particles called “gluons.” – “Sea quarks” are also present: short-lived quark-

antiquark pairs from quantum mechanical fluctuations.

• As you hit the proton with more energy, you resolve shorter-lived fluctuations: gluons and sea quarks.

The simplest model says a proton’s made of three “valence” quarks: 2 up quarks and 1 down quark.


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Strong Force

• How does the nucleus stay together? The electromagnetic force should cause the protons to repel one another . . .

• Protons and neutrons interact via the strong force, carried by gluons– Much stronger than the electromagnetic force (thus

the name!)– But very short range! (~10-15 m)


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Color Charge and QCD

• Strong force acts on particles with color charge– Quarks, plus gluons themselves! (Contrast with

photons, which are electrically neutral)

• “Color” because three different “charges” combine to make a neutral particle: red+blue+green = white

• Quantum Chromodynamics (QCD)—theory describing the strong force

Note that quarks also carry fractional electromagnetic charge!Proton = up + up + down quarks +1 = +2/3 + +2/3 + -1/3

Neutron = down + down + up 0 = -1/3 + -1/3 + +2/3


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Quark Confinement

• Never see quarks or gluons directly!– Confined to composite, color-neutral particles– Groups of three quarks (rgb), called baryons, or

quark-antiquark pairs (red-antired, . . .), called mesons

• If you try to pull two quarks apart, energy between them increases until you produce a new quark-antiquark pair (recall E=mc2)

“D- meson”

“D+ meson”


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For More Information

• For more info on quarks, gluons, and the strong force, see

http://www.particleadventure.org/(Many pictures on previous pages borrowed from

this site)


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Studying Proton Structure

• If can’t see individual quarks and gluons (“partons”), how to determine the proton’s structure?

• Inelastic scattering—shoot a high-energy beam (e.g. of electrons) at the proton to break it up, and try to understand what happens– Electron exchanges a photon with quarks, because quarks

carry electromagnetic charge as well as color

Describe proton structure in terms of parton distribution functions (pdf’s) - Probability of scattering off of a parton carrying a particular fraction of the proton’s momentum (“Bjorken-x” variable)

(Recall that even if protons are in a stationary target, have non-zero momentum in center-of-mass frame)


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Proton Structure and Momentum Fraction

Halzen and Martin, “Quarks and Leptons,” p. 201

xBj

xBj

1

xBj11

1/3

1/3

xBj

1/3 1

Valence

Sea

A point particle

3 valence quarks

3 bound valence quarks

3 bound valence quarks and some slow sea quarks

Slow

What momentum fraction would the scattering particle carry if the proton were made of …


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What Have We Learned?

• Conclusions from decades of inelastic scattering data investigating proton momentum structure:– 3 “valence” quarks carry (on average) the largest

single momentum fractions of the proton– But lots of gluons and “sea” quark-antiquark pairs in

the proton as well! Gluons carry ~50% of total momentum of proton.

What about the spin structure of the proton?

- Do inelastic scattering with polarized protons! (spin directions all aligned)

~ ~ ?


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q

q

g

Proton

u u

d

p

Surprising data from late 1980’s!

1987: Only 14% +- 23% of proton’s spin carried by quarks’ spins!

The Proton Spin Crisis begins!!

Spin zLG 2

1

2

1Quark Spin Gluon

Spin

Orbital Angular Momentum

The Proton Spin Crisis

Say you have a proton with total spin +1/2 along some axis. Most naively, you’d expect it to contain two quarks with spin +1/2 and one with spin -1/2.1/2 + 1/2 - 1/2 = +1/2

gluo

n

These haven’t been easy to measure!


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Polarized Parton Distribution Functions• Describe spin structure in terms of polarized

parton distribution functions

• Helicity distributions—difference in probability of scattering off of a quark or gluon with same vs. opposite helicity of proton

Helicity: Projection of spin vector onto momentum vector for particles polarized longitudinally, i.e. parallel to direction of motion.

Either positive or negative.

Positive helicity

Negative helicity

vs.


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Quark and Gluon Helicity Distributions

up quarks

down quarks

sea quarks

gluon

EMC, SMC at CERN E142 to E155 at SLACHERMES at DESY

In valence region (xBj>~0.1), note up quarks have large spin contribution in same direction as proton spin and down quarks have (smaller) contribution opposite to proton - Reminiscent of ½ + ½ - ½ = ½, but numbers don’t add up!

Sea quarks just add to our difficulties!!

Can gluon spin account for what’s missing??xBj xBj

We’re trying to find out at RHIC!


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The Relativistic Heavy Ion Collider• Two main physics programs: Proton spin

structure + QCD at high energies and densities

• Heavy-ion program: Search and discovery mission for quark-gluon plasma, state of matter believed to have existed 10 millionths of a second after the Big Bang.

• First polarized proton collider in world! Special magnets and other equipment installed to maintain and measure polarization.


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RHIC at Brookhaven National Laboratory

The Relativistic Heavy Ion Collider

located at Brookhaven National Laboratory

Long Island,

New York


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The Relativistic Heavy Ion Collider• Heavy ions, polarized

protons• Most versatile collider

in the world! Nearly any species can be collided with any other.– asymmetric species

possible due to independent rings with separate steering magnets (unlike matter-antimatter colliders)


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AGSLINACBOOSTER

Polarized Source

Spin Rotators

200 MeV Polarimeter

AGS Internal Polarimeter

Rf Dipole

RHIC pC Polarimeters Absolute Polarimeter (H jet)

PHENIX

PHOBOS BRAHMS & PP2PP

STAR

AGS pC Polarimeter

Partial Snake

Siberian Snakes

Siberian Snakes

Helical Partial SnakeStrong Snake

Spin Flipper

RHIC as a Polarized p+p Collider

Various equipment to maintainmaintain and measuremeasure beam polarization through acceleration and storage


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RHIC’s Experiments

Transverse spin only (No rotators)

Longitudinal or transverse spin

Longitudinal or transverse spin


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PHENIX 14 Countries; 69 Institutions; > 500 Participants as of July 2007


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PHENIX Detector

2 central arms- Track charged particles and detect electromagnetic processes

2 forward arms- Identify and track muons (“heavy electrons”)

Philosophy: Fast data acquisition & high granularity Trade-off area covered


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PHENIX Detector


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Au+Au Collision in PHENIX Central Arms


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Fixed-Target Vs. Collider Experiments

• Earliest experiments studying proton structure used electron beams to probe stationary (“fixed”) proton targets (think of tube of hydrogen gas)– Typically easier and cheaper to perform fixed-target

experiments

• Collider experiments allow you to reach higher energy– Can use different theoretical tools to interpret results

(“perturbative QCD” = “pQCD”)– Can produce heavier particles (E=mc2 again!)– Can access different kinematic region (e.g. lower momentum

fraction, xBj)


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Proton-Proton Scattering Vs. Electron-Proton Scattering

• Studying the proton by breaking it up with another proton is much more complicated than probing it with an electron beam!– Two composite objects colliding and breaking up

• Rely on some input from experiments performed in simpler systems

• One specific advantage: Direct access to gluons, which cannot be probed directly via electron beams (no electromagnetic charge)


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Hard Scattering Process

2P2 2x P

1P

1 1x P

s

qgqg

)(0

zDq

X

q(x1)

g(x2)

Understanding Particle Production in p+p Collisions

Particle production rates can be calculated using pQCD from:– Parton distribution functions (from experiment)

– pQCD partonic scattering rates (from theory)

– “Fragmentation functions” (from experiment)

Un

iversa

lity

)(ˆˆ0

210 zDsxgxqXpp q

qgqg

Can use factorized perturbative QCD (pQCD) to calculate particle production at high-energy facilities


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How Well Does Factorized pQCD Work at RHIC?

g2 gq q2

2P2 2x P

1P

1 1x P

Fraction pions produced ~90o from beam

0

pT (GeV/c)

pQCD calculations describe polarization-averaged cross-section measurements well at RHIC!

pT: Transverse momentum.Interesting because if scattered quarks and gluons change direction sharply with respect to the beam direction, we know there was a “hard” interaction! (Think of Rutherford)


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How Can We Investigate the Proton’s Spin at RHIC?

• Collide polarized protons in different configurations and see what we observe in our detector

• Most often examining asymmetries– e.g. difference in the number of a certain particle produced when the

beams have the same vs. opposite polarization– Same number produced gives asymmetry = 0.– All from one configuration and none from the other gives +1 or -1.

• Knowing what partonic processes (involving quarks and gluons) led to production of the observed particle gives us a handle on the quarks’ and gluons’ contribution to the spin.

CB

CBAsymmetry


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Hard Scattering in Polarized p+p

Asymmetry

qg qˆ

Hard Scattering Process

2P2 2x P

g 2f x

q 1f x1P

1 1x P

zhqD

s

1ps

2ps

)(ˆˆ0

210 zDsxgxqXpp q

qgqg

Measure asymmetries, input q as measured by previous experiments, then use pQCD to “solve for” g, the gluon spin contribution to the proton’s spin


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Some Spin Asymmetry Measurements

• ALL: “double-longitudinal” asymmetry measurement, taken with both beams longitudinally polarized, sensitive to the gluon spin contribution to the proton’s spin

spin oppspin same

spin oppspin same

~NN

NNALL


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ALL of Neutral PionsData show asymmetry close to zero.

Different curves are theoretical predictions assuming different values of g.


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ALL of Charged PionsPrediction of ordering of pion

asymmetries depending on sign of gluon spin contribution.

LLLLLL AAAg

0

0

Not yet clear. Need more data! …


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Measuring Asymmetries at Other Energies

• Measuring asymmetries at different energies accesses different ranges of momentum fraction– Lower energies Higher momentum fractions– Higher energies Lower momentum fractions

• So far most data taken at 200 GeV

• Short run in 2006 at 62.4 GeV

• Future running at 500 GeV planned

Also working on charged

particle asymmetry


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A Global Effort• No single measurement can determine proton spin

structure– Trying to map out these polarized parton distribution functions,

need to measure the functions at different momentum fraction values

• RHIC spin experiments are continuing the work of earlier ones, which started in the mid-1980s

• Two other spin experiments ongoing– HERMES (Hamburg, Germany): electron-proton fixed-target– COMPASS (Geneva, Switzerland): muon (heavy electron)-

proton fixed-target• Future experiments

– Proposed Electron-Ion Collider at RHIC or Jefferson Lab– . . .

Hope to pin down the parton distribution functions by putting all world data together

up quarks

down quarks

sea quarks

gluon


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Gluon Spin from Various Global Analyses

xΔg(x) atQ2 = 10 GeV2

Latest analysis!


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Latest Global Analysis of Helicity Distributions

• “DSSV” the first global analysis to include RHIC data on an equal footing with all other world data

• Finds small gluon spin contribution, with distribution crossing zero near x ~ 0.1!

de Florian, Sassot, Stratmann, Vogelsang

Look forward to even better knowledge of gluon spin contribution to proton spin as further RHIC (and other) data

become available!


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Longitudinal vs. Transverse Spin Structure

• Transverse spin structure of the proton cannot be deduced from longitudinal (helicity) structure– Spatial rotations and Lorentz boosts don’t commute

– Relationship between longitudinal and transverse structure provides information on the relativistic nature of partons in the proton

• Transverse spin structure of the proton remains much less well understood than longitudinal, but field advancing rapidly!– Measurements in p+p increasingly valuable, as necessary

“input” quantities from simpler systems become available

Quark “transversity” distribution


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The Whole Story??

• Not yet! A number of years to go . . .• Present RHIC data suggest gluon spin contribution to

proton spin can’t make up what’s missing!– Proton Spin Crisis continues!!!

• If there are no surprises at low momentum fractions, orbital angular momentum of quarks and gluons the only possibility left, but nobody knows how to measure it directly!– Any suggestions?? Spin zLG

2

1

2

1Quark Spin Gluon

Spin

Orbital Angular Momentum


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Extra Slides


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• Fermions include most of the familiar matter around us, such as electrons, protons, and neutrons, as well as others.

Fermions and BosonsAll particles can be classified into two categories depending on their spin: fermions and bosons.

• Bosons include force-carrier particles such as the photon (electromagnetic force) and gluon (strong force), plus composite particles made of an even number of fermions.


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Factorization in pQCD

Parton distribution functions (need experimental input)

- probability of scattering off of a gluon or particular flavor quark carrying a certain momentum fraction of the proton momentum

- easiest to measure in electron-proton scattering measurements

pQCD hard scattering rates (calculable in pQCD)

- scattering rates for quarks on quarks, quarks on gluons, or gluons on gluons

- calculate theoretically

Fragmentation functions (need experimental input)

- probability of a particular flavor quark “fragmenting” into (becoming) a particular final-state particle (remember you never see an individual quark!)

)(ˆˆ0

210 zDsxgxqXpp q

qgqg


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ALL of 0 at Two Energies


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+, - ALL and g

• At transverse momentum > ~5 GeV/c, pions are dominantly produced via qg scattering

• The tendency of + to fragment from an up quark and - from a down quark and the fact that u and d have opposite signs make ALL of + and - differ measurably

• This difference can allow us to determine the sign of g

)( du

)( ud

LLLLLL AAAg

0

0


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ALL of Charged Pions (STAR)

Documents

UMass Amherst Christine A. Aidala The Whole Story Behind a Half: The Quest to Understand the Proton’s Spin Sambamurti Memorial Lecture BNL July 22, 2008