Carl Gagliardi Outline - Cyclotron Institute lecture notes/gagliardi_reu_2012.pdfWhat makes the...

What makes the proton spin?Carl Gagliardi

Texas A&M University

Outline• Atomic structure• Particle spin• Proton structure• Proton spin

What makes the proton spin? – Carl Gagliardi 2

Looking inside the atom

• J. J. Thompson discovered the electron in 1897– Found electrons are components of all atoms– Found the electron mass is <0.1% of atomic masses

• Formulated the “plum pudding” model of the atom in 1904– Light negative electrons embedded in a distributed

massive positive charge

Typical atomic radius:Few x 10-10 m


Geiger-Marsden experiment (1909)

• Shoot energetic alpha particles at a very thin gold foil• Measure the deflection of the alpha particles as they pass through• Expected:

– Alpha particles will be deflected by only a few degrees


Geiger-Marsden experiment (1909)

• Shoot energetic alpha particles at a very thin gold foil• Measure the deflection of the alpha particles as they pass through• Found:

– Most alpha particles are deflected by only a few degrees– Some alpha particles are deflected through large angles– A few alpha particles bounce backwards toward the source


Ernest Rutherford’s explanation (1911)

• The atom consists of a very dense, positively charged nucleus (radius of a few x 10-15 m) with the light electrons orbiting at typical radii of a few x 10-10 m

“It was quite the most incredible event that has ever happened to me in my life. It was almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you.”


Stern-Gerlach experiment (1922)

• Pass a beam of Ag atoms through a non-uniform magnetic field

• Each Ag atom possesses a magnetic moment

• Classical expectation:– Atoms will spread into a

broad spot


Stern-Gerlach experiment (1922)

• Experimental observation:– Atomic beam split into two separate components

• The magnetic moment of the Ag atom can only point in two possible directions

• Discovery of spin


Pauli exclusion principle (1924)

• Chemists had concluded that rows of the periodic table involve filling certain electron shells

• Various rows take different “magic numbers” of electrons (2, 8, 8, 18, …)• Pauli looked for a way to systematize these empirical observations• “No two electrons can have all the same quantum numbers”

– For vintage-1925 quantum mechanics, this gave 1, 4, 4, 9, ...• Assumed the existence of a new quantum number for electrons that

could only take on 2 values in order to double all of these– Electron spin provided a natural explanation


What is spin?• Fundamental property of particles in quantum mechanics• For the electron, the spin takes on one of two possible values:

– +1/2 ћ or +5.27 x 10-35 J s– -1/2 ћ or -5.27 x 10-35 J s

• Often imagine a spinning top– Handy model to gain intuition– Not correct in detail– The electron spin has no true analog in the classical world

of objects moving under the influence of Newton’s Laws


Importance of structure

• Rutherford’s insight into the structure of the atom, together with Pauli’s “exclusion principle” which works the way it does because of electron spin, have given us a detailed understanding of the chemical properties of the elements


What about the proton?

• Charge (1.60 x 10-19 C) is exactly opposite that of the electron• Mass (1.67 x 10-27 kg) is 1836 times that of the electron • Spin (+ or -1/2 ћ or 5.27 x 10-35 J s) has exactly the same magnitude

as the electron

• Proton magnetic moment is “too big” by a factor of 2.79– Must be a composite object (unlike the electron)

• Radius ~ 0.85 x 10-15 m

• What is the internal structure of the proton?


High energy proton-antiproton scattering

• Scattering extends to very large angles, similar to that found by Geiger and Marsden for alpha particles on gold

• Proton also composed of much smaller constituents– Quarks and gluons– How are they combined together?


The proton in the quark model

• The proton is made of quarks• 2 up quarks (charge = +2/3) and 1 down quark (charge =

-1/3) provide the proton charge and spin

• Quarks are bound together by gluons (charge = 0)

u u

d


Proton wavefunction in the static quark model

• If mu = md = mp/3. Then:• Proton magnetic moment:

– Calculate +3 μN; find +2.793 μN• Neutron magnetic moment:

– Calculate -2 μN; find -1.913 μN• Ratio matches prediction to ~3%

))()((181))()((

181))()((

92

))()((181))()((

181))()((

92

))()((181))()((

181))()((

92

↓↑↑−↑↑↓−↑↓↑

+↑↓↑−↓↑↑−↑↑↓

+↑↑↓−↑↓↑−↓↑↑

uduuduudu

uuduuduud

duuduuduu

x (totally anti-symmetric color wavefunction)

If assume quarks are slightly heavier to allow for some binding energy, can match the observed magnetic moments very well


Too good to be true• The proton radius is ~0.85 fm• Heisenberg Uncertainty Principle implies quark motion must be

relativistic• Relativistic quark model

– Quarks are no longer restricted to s-wave states– Quark spin accounts for ~60% of the proton spin– Rest of proton spin comes from quark orbital angular momentum

• No binding force in these calculations

• Strong force (Quantum Chromodynamics) provides the quark binding– Gluons must also be present– Can also have additional quark-antiquark pairs


Looking inside the proton

• “Deep-inelastic scattering” (DIS) of electrons and muons off protons has taught us a great deal about the internal structure of the proton

• Interaction is electromagnetic only quarks and anti-quarks participate directly

• Obtain information about gluons indirectly

p

e or μ

q or q

γ*


Parton distribution functions

• Probability of finding a quark or gluon inside the proton carrying a fraction x of the total momentum of the proton

• Find more gluons than anything else• Gluons carry half the momentum of the proton


Microscopic origin of the proton spin

• Measure deep-inelastic scattering with polarized electrons or muonsoff polarized protons

• Difference in cross section for like vs. unlike helicity beams provides information about spin orientations of the quarks inside the polarized proton

p

e or μ

q or qe or μ p

⇒

⇒

⇒

γ* q or qsz = +1 Helicity + or - ?

γ*


Proton “spin crisis”

• First measurement over a broad kinematic region was performed bythe European Muon Collaboration in the mid-’80s

• Found that quarks contribute only (14 ± 9 ± 21)% of the proton spin

EMC, PLB 206, 364


Since EMC

• Many subsequent measurements• Results are well described by “global analyses” that find best-fit polarized parton distribution functions

• Polarization of u+u and d+d quarks well determined– Individual u, u, d, d polarizations have much larger uncertainty

• Only ~30% of the proton spin arises from quarks and antiquarks

DSSV, PRD 80, 034030


What about gluon polarization?

Three fits of equal quality:– ΔG = 0.13 ± 0.16– ΔG ~ 0.006– ΔG = -0.20 ± 0.41all at Q2 = 1 GeV2

Leader et al, PRD 75, 074027

Kinematic region of polarized measurements


What contributes to the proton spin?Consider a proton moving

toward the right

HelicityΔq(x)Δg(x)

Transversityδq(x)

Proton spin ⇒⇒ ⇐

Proton spin ⇑

⇑ ⇓

Spin sum rule: ⟩⟨++==⟩⟨ LGS pz ΔΔΣ

21

21

Polarized DIS: ~ 0.3 Poorly constrained

Very little data

RHIC spin program:Exploring poorly determined components of the proton

Anselmino et al, arXiv:0812.4366


p + p collisions in perturbative QCD

p

p

dcbabbaa QxfQxf +→+∑= σσ ˆ),(),( 22

a, xa P

b, xb P

fa

fb

c

d

Parton distribution functions

pQCD hard scatter

a

b

Jet

Jet

a and b can be quarks, gluons, or a combination


LLba

baLL a

ffffA ˆΔΔ

∝+−

= −+++

−+++

σσσσ

Δf: polarized parton distribution functions

∗θcos

For most RHIC kinematics, gg and qgdominate, making ALL sensitive to gluon polarization.

10 20 30 pT(GeV)

Partonic fractions in jet production at 200 GeV

0

Exploring gluon polarization at RHIC


Separating quark and anti-quark polarizations

Measure parity violating single helicity asymmetry AL(Helicity flip in one beam while averaging over the other)

u + d → W + → e+ + ν

u + d → W − → e− + ν

ALW +

∝−Δu(x1)d (x2) + Δd (x1)u(x2)ALW − ∝−Δd(x1)u (x2) + Δu (x1)d(x2)

• Weak interaction process– Only left-handed quarks– Only right-handed anti-quarks

• Perfect spin separation


RHIC: the world’s first (and only!) polarized hadron collider

• Spin varies from rf bucket to rf bucket (9.4 MHz)• Spin pattern changes from fill to fill• Spin rotators provide choice of spin orientation• Billions of spin reversals during a fill with little depolarization

BRAHMS

PHENIX

AGS

BOOSTER

Spin Rotators(longitudinal polarization)

Solenoid Partial Siberian Snake

Siberian Snakes

200 MeV PolarimeterAGS Internal Polarimeter

Rf Dipole

RHIC pC PolarimetersAbsolute Polarimeter (H↑ jet)

AGS pC Polarimeters

Strong Helical AGS Snake

Helical Partial Siberian Snake

Spin Rotators(longitudinal polarization)

Spin flipper

Siberian Snakes

STAR

PHOBOS

Pol. H- SourceLINAC


Kinematics for colliders

pT

p|| θ

( )[ ]2tanln θη −=Pseudo-rapidity:

Transverse momentum (pT) and pseudorapidity (η)provide a convenient description

Mid-rapidity: η = 0, perpendicular to the incident beamsη = 1: Scattering at θ ~ 400 in the CM (or lab) frameη = 4: Scattering at θ ~ 20 in the CM (or lab) frame

)cosh()sinh(

ηη

Ttot

Tz

pppp

==


Essential benchmark – unpolarized cross sections

• Mid-rapidity jet cross section is consistent with NLO pQCD over 7 orders of magnitude

• Forward rapidity π0 cross section also consistent with NLO pQCD• Many other examples• pQCD works over a very broad kinematic range at RHIC energies

STARSTAR PRL 97, 252001 STARSTAR PRL 97, 152302


What’s needed to determine ALL?

• Three concurrent measurements:– Beam polarizations– Relative luminosities– Event yields

• AL is done similarly, but with one beam polarized and one unpolarized

−+++

−+++

+−

=RNNRNN

PPALL

21

1−+

++=LLR

N++: yield when helcities same

where

N+−: yield when helcities opposite


Measuring the polarization

• p-Carbon– Quick measurements– Determine beam polarization and intensity profiles– Multiple measurements give time dependence during a fill– Only give relative measurements

• H Jet– Circulating beams scatter off a polarized H atomic beam

• Atomic beam polarization known with high precision– Provides absolute determination of the circulating beam

polarizations averaged over each fill

BRAHMS

Siberian Snakes

RHIC pC PolarimetersAbsolute Polarimeter (H↑ jet)

Siberian Snakes

PHOBOS


E-M Calorimeter

Time of Flight

Projection Chamber

Relative luminosities and event yields: STAR detector


What are we learning?


STAR inclusive jet ALL from 2006

STARSTAR

• STAR inclusive jet ALL excludes those scenarios that have a large gluon polarization within the accessible x region


DSSV – first global analysis with polarized jets

• The first global NLO analysis to include inclusive DIS, SIDIS, and RHIC pp data on an equal footing

de Florian et al., PRL 101, 072001

STAR


ALL for inclusive jets: 2006 to 2009

• 2009 STAR inclusive jet ALL measurements are a factor of 3 (high-pT) to >4 (low-pT) more precise than 2006

• Results fall between predictions from DSSV and GRSV-STD

STARSTAR


Beyond inclusive ALL measurements

• Inclusive ALL measurements at fixed pT average over a broad x range.• Can hide considerable structure if Δg(x) has a node• Di-jet measurements can constrain the shape of Δg(x)

STARSTAR PRL 100, 232003


p + p collisions in perturbative QCD

p

p

a, xa P

b, xb P

fa

fb

c

d

a

b

Jet

Jet

⎟⎠⎞

⎜⎝⎛ +

±=2

exp 4321

ηηs

Mx,x

• Di-jets provide direct access to parton kinematics at leading order


2009 STAR di-jet partonic coverage

STARSTAR

( )

( )

2tanhcos

2ln

21

|ηη||θ|

ηηxxy

sxxM

epeps

1x

epeps

1x

43*

43

2

1

21

ηT,4

ηT,32

ηT,4

ηT,31

43

43

−=

+==

=

+=

+=

−−

xx


2009 STAR di-jet ALL

• For fixed M, different kinematic regions sample different x ranges• ALL falls between DSSV and GRSV-STD

• Taken together, the 2009 STAR jet and di-jet ALL measurementspoint toward a positive gluon spin contribution to the proton spin

STARSTAR


First STAR W AL

STAR 2009 ResultAL (W +) = −0.27 ± 0.10(stat) ± 0.02(syst)AL (W −) = 0.14 ± 0.19(stat) ± 0.02(syst)

Lepton pseudorapidity

STARSTAR PRL 106, 062002


Anticipated W sensitivity in the near future

• Measurements over the next couple of years will provide substantial constraints on the antiquark polarization in the proton


Transverse single-spin asymmetries at forward rapidity

• Large single-spin asymmetries at CM energies of 20 and 200 GeV

STARSTAR

Parton orbital motion Transversity

TqSN /pmαA ∝

PRL 101, 222001

• Weren’t supposed to be there in naïve pQCD

• May arise from the Sivers effect, Collins effect, or a combination


Sivers and Collins effects in deep-inelastic scattering

• Semi-inclusive DIS can distinguish the Sivers and Collins effects• HERMES finds both are non-zero• COMPASS finds consistent Collins effects; smaller Sivers effects

A. Airapetian et al (HERMES)

Sivers Collins


Sivers and Collins effects in pp collisions

Collins mechanism: asymmetry in the forward jet fragmentation

Sivers mechanism: asymmetry in the forward jet production

SP kT,q

p

p

SP

p

p

Sq kT,πSensitive to proton spin –parton transverse motioncorrelations

Sensitive to transversity

• Need to go beyond inclusive hadrons

• Limited (no more?) time: focus on jet measurements of transversity


Observing the Collins effect in jets

• A spin-dependent azimuthal variation in hadron production around the jet thrust axis

• Alternative approach: Interference Fragmentation Function (IFF)– Di-hadron as surrogate for the jet– Examine di-hadron relative angle, measured around the pair

momentum


Leading pions in mid-rapidity jets

• Azimuthal asymmetries measured within fully reconstructed jets• Average asymmetries:

– π+ = 0.021 +/- 0.006 +/- 0.023– π- = -0.004 +/- 0.007 +/- 0.023– Expected asymmetry from global analysis ~ +/- 0.07


Mid-rapidity interference fragmentation functions

• Clear signature of quark transversity in p+p collisions at RHIC

π+ π- IFF

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

-1.0 -0.5 0.0 0.5 1.0

cos theta*

D_T

T

q+q --> q+qq+g --> q+g or g+qq+q' --> q+q' or q'+q

π+ π- IFF


Conclusions

• We still have a great deal to learn about the structure of the proton

• RHIC is making significant contributions to three poorly constrained pieces of the puzzle– Gluon polarization– Flavor-separated quark and anti-quark polarizations– Transversity

• All the measurements that I’ve shown will be extended substantiallyover the next few years. Stay tuned!

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