Post on 13-Jul-2020
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
What makes the proton spin? – Carl Gagliardi 3
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
What makes the proton spin? – Carl Gagliardi 4
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
What makes the proton spin? – Carl Gagliardi 5
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.”
What makes the proton spin? – Carl Gagliardi 6
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
What makes the proton spin? – Carl Gagliardi 7
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
What makes the proton spin? – Carl Gagliardi 8
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 makes the proton spin? – Carl Gagliardi 9
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
What makes the proton spin? – Carl Gagliardi 10
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 makes the proton spin? – Carl Gagliardi 11
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?
What makes the proton spin? – Carl Gagliardi 12
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?
What makes the proton spin? – Carl Gagliardi 13
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
What makes the proton spin? – Carl Gagliardi 14
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
What makes the proton spin? – Carl Gagliardi 15
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
What makes the proton spin? – Carl Gagliardi 16
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*
What makes the proton spin? – Carl Gagliardi 17
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
What makes the proton spin? – Carl Gagliardi 18
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*
What makes the proton spin? – Carl Gagliardi 19
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
What makes the proton spin? – Carl Gagliardi 20
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 makes the proton spin? – Carl Gagliardi 21
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 makes the proton spin? – Carl Gagliardi 22
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
What makes the proton spin? – Carl Gagliardi 23
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
What makes the proton spin? – Carl Gagliardi 24
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
What makes the proton spin? – Carl Gagliardi 25
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
What makes the proton spin? – Carl Gagliardi 26
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
What makes the proton spin? – Carl Gagliardi 27
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
==
What makes the proton spin? – Carl Gagliardi 28
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 makes the proton spin? – Carl Gagliardi 29
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
What makes the proton spin? – Carl Gagliardi 30
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
What makes the proton spin? – Carl Gagliardi 31
E-M Calorimeter
Time of Flight
Projection Chamber
Relative luminosities and event yields: STAR detector
What makes the proton spin? – Carl Gagliardi 32
What are we learning?
What makes the proton spin? – Carl Gagliardi 33
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
What makes the proton spin? – Carl Gagliardi 34
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
What makes the proton spin? – Carl Gagliardi 35
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
What makes the proton spin? – Carl Gagliardi 36
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
What makes the proton spin? – Carl Gagliardi 37
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
What makes the proton spin? – Carl Gagliardi 38
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
What makes the proton spin? – Carl Gagliardi 39
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
What makes the proton spin? – Carl Gagliardi 40
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
What makes the proton spin? – Carl Gagliardi 41
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
What makes the proton spin? – Carl Gagliardi 42
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
What makes the proton spin? – Carl Gagliardi 43
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
What makes the proton spin? – Carl Gagliardi 44
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
What makes the proton spin? – Carl Gagliardi 45
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
What makes the proton spin? – Carl Gagliardi 46
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
What makes the proton spin? – Carl Gagliardi 47
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
What makes the proton spin? – Carl Gagliardi 48
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!