What makes the ?

Carl Gagliardi Texas A&M University Outline • Atomic structure • Particle spin • Proton structure •Proton spin Looking inside the atom

Typical atomic radius: Few x 10-10 m

• 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

What makes the proton spin? – Carl Gagliardi 2 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 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 • 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 4 Ernest Rutherford’s explanation (1911)

“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.”

• 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

What makes the proton spin? – Carl Gagliardi 5 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 6 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 7 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 8 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 9 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 10 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 11 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 – and – How are they combined together?

What makes the proton spin? – Carl Gagliardi 12 The proton in the model

u u

d

• The proton is made of quarks •2 up quarks (charge = +2/3) and 1 (charge = -1/3) provide the proton charge and spin

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

What makes the proton spin? – Carl Gagliardi 13 Proton wavefunction in the static quark model

2 1 1 (u ↑)(u ↑)(d ↓) − (u ↑)(u ↓)(d ↑) − (u ↓)(u ↑)(d ↑) + 9 18 18 2 1 1 (d ↓)(u ↑)(u ↑) − (d ↑)(u ↑)(u ↓) − (d ↑)(u ↓)(u ↑) + 9 18 18 2 1 1 (u ↑)(d ↓)(u ↑) − (u ↓)(d ↑)(u ↑) − (u ↑)(d ↑)(u ↓) 9 18 18 x (totally anti-symmetric color wavefunction)

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

– Calculate +3 μN; find +2.793 μN • Neutron magnetic moment: – Calculate -2 μ ; find -1.913 μ If assume quarks are slightly N N heavier to allow for some binding • Ratio matches prediction to ~3% energy, can match the observed magnetic moments very well

What makes the proton spin? – Carl Gagliardi 14 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

• No binding force in these calculations

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

What makes the proton spin? – Carl Gagliardi 15 Looking inside the proton

e or μ

γ*

q or q p

• “Deep-inelastic scattering” (DIS) of electrons and off has taught us a great deal about the internal structure of the proton • Interaction is electromagnetic Æ only quarks and anti-quarks participate directly • Obtain information about gluons indirectly

What makes the proton spin? – Carl Gagliardi 16 Parton distribution functions

• Probability of finding a quark or 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 17 Microscopic origin of the proton spin e or μ

γ*

q or q ⇒ ⇒ ⇒ p e or μ p

sz = +1 Helicity + or - ? γ* q or q

• Measure deep-inelastic scattering with polarized electrons or muons off polarized protons • Difference in cross section for like vs. unlike helicity beams provides information about spin orientations of the quarks inside the polarized proton What makes the proton spin? – Carl Gagliardi 18 Proton “spin crisis”

EMC, PLB 206, 364

• First measurement over a broad kinematic region was performed by the European Collaboration in the mid-’80s • Found that quarks contribute only (14 ± 9 ± 21)% of the proton spin

What makes the proton spin? – Carl Gagliardi 19 Since EMC DSSV, PRD 80, 034030

• 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

What makes the proton spin? – Carl Gagliardi 20 What about gluon polarization?

Three fits of equal quality: – ΔG = 0.13 ± 0.16 – ΔG ~ 0.006 Kinematic region of – ΔG = -0.20 ± 0.41 2 2 polarized measurements all at Q = 1 GeV Leader et al, PRD 75, 074027

What makes the proton spin? – Carl Gagliardi 21 What contributes to the proton spin?

Consider a proton moving toward the right

Proton spin ⇒ Helicity ⇒ ⇐ Δq(x) Δg(x)

Polarized DIS: ~ 0.3 Poorly constrainedAnselmino et al, arXiv:0812.4366

1 1 Spin sum rule: 〈 S p 〉 = = ΔΣ + ΔG + 〈 L〉 z 2 2 Proton spin ⇑ Transversity RHIC spin program: δq(x) ⇑ ⇓ Exploring poorly determined components of the proton Very little data

What makes the proton spin? – Carl Gagliardi 22 p + p collisions in perturbative QCD

p Jet

a, xa P fa a c

d b σ Jet b, x P fb b pQCD hard scatter p

= f (x ,Q 2 ) f (x ,Q 2 )σˆ ∑ a a b b a+b→c+d a and b can be quarks, gluons, Parton distribution functions or a combination

What makes the proton spin? – Carl Gagliardi 23 σ Exploring gluon polarization at RHIC ++ −σ +− Δf Δf σ a b ALL = ++ +− ∝ aˆ LL + σ f a fb Δf: polarized parton distribution functions

Partonic fractions in jet production at 200 GeV

cosθ ∗ For most RHIC kinematics, gg and qg

dominate, making ALL sensitive to gluon polarization. 0 10 20 30 pT(GeV)

What makes the proton spin? – Carl Gagliardi 24 Separating quark and anti-quark polarizations

u + d → W + → e+ + ν u + d → W − → e− + ν

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

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

+ W − W AL ∝−Δd(x1)u (x2) + Δu (x1)d(x2) AL ∝−Δu(x1)d (x2) +Δd (x1)u(x2)

What makes the proton spin? – Carl Gagliardi 25 RHIC: the world’s first (and only!) polarized hadron collider

Absolute Polarimeter (H↑ jet) RHIC pC Polarimeters

PHOBOS BRAHMS

Siberian Snakes Siberian Snakes PHENIX

STAR

Spin Rotators Spin flipper (longitudinal polarization) - Spin Rotators Pol. H Source Solenoid Partial Siberian Snake (longitudinal polarization) LINAC BOOSTER Helical Partial Siberian Snake AGS Internal Polarimeter AGS 200 MeV Polarimeter AGS pC Polarimeters Rf Dipole Strong Helical AGS Snake • 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

What makes the proton spin? – Carl Gagliardi 26 Kinematics for pT colliders θ

p||

Pseudo-rapidity: η = −ln[]tan(θ 2)

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

pz = pT sinh(η)

ptot = pT cosh(η)

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

What makes the proton spin? – Carl Gagliardi 27 Essential benchmark – unpolarized cross sections

STAR PRL 97, 252001 STAR PRL 97, 152302

• 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 What makes the proton spin? – Carl Gagliardi 28 What’s needed to determine ALL?

N++: yield when helcities same

N+−: yield when helcities opposite

1 N ++ − RN+− L++ ALL = where R = P1P2 N ++ + RN+− L+−

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

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

What makes the proton spin? – Carl Gagliardi 29 Measuring the polarization

Absolute Polarimeter (H↑ jet) RHIC pC Polarimeters PHOBOS BRAHMS

Siberian Snakes Siberian Snakes

•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

What makes the proton spin? – Carl Gagliardi 30 Relative luminosities and event yields: STAR detector

E-M Calorimeter

Projection Chamber

Time of Flight

What makes the proton spin? – Carl Gagliardi 31 What are we learning?

What makes the proton spin? – Carl Gagliardi 32 STAR inclusive jet ALL from 2006

STAR

• 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 33 DSSV – first global analysis with polarized jets de Florian et al., PRL 101, 072001

STAR

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

What makes the proton spin? – Carl Gagliardi 34 ALL for inclusive jets: 2006 to 2009 STAR

• 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

What makes the proton spin? – Carl Gagliardi 35 Beyond inclusive ALL measurements

STAR PRL 100, 232003

• 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)

What makes the proton spin? – Carl Gagliardi 36 p + p collisions in perturbative QCD

p Jet

a, xa P fa a c

d b Jet b, xb P fb p M ⎛ η3 + η4 ⎞ x1 , x2 = exp⎜± ⎟ s ⎝ 2 ⎠

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

What makes the proton spin? – Carl Gagliardi 37 2009 STAR di-jet partonic coverage

STAR

x x

1 η3 η4 x1 = ()pT,3e + pT,4e s

1 −η3 −η4 x2 = ()pT,3e + pT,4e s

M = x1 x2 s 1 x η + η y = ln 1 = 3 4 2 x2 2 | η − η | | cosθ* |= tanh 3 4 2

What makes the proton spin? – Carl Gagliardi 38 2009 STAR di-jet ALL STAR

• 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 measurements point toward a positive gluon spin contribution to the proton spin

What makes the proton spin? – Carl Gagliardi 39 First STAR W AL

STAR PRL 106, 062002

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

Lepton pseudorapidity

What makes the proton spin? – Carl Gagliardi 40 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 41 Transverse single-spin asymmetries at forward rapidity

STAR PRL 101, 222001

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

• Weren’t supposed to be there in naïve pQCD AN ∝ αSmq /pT • May arise from the Sivers effect, Collins effect, or a combination Parton orbital Transversity motion What makes the proton spin? – Carl Gagliardi 42 Sivers and Collins effects in deep-inelastic scattering

A. Airapetian et al (HERMES)

Sivers Collins

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

What makes the proton spin? – Carl Gagliardi 43 Sivers and Collins effects in pp collisions

Sivers mechanism: asymmetry Collins mechanism: asymmetry in the forward jet production in the forward jet fragmentation

SP SP kT,q

p p

p p

Sq kT,π Sensitive to proton spin – Sensitive to parton transverse motion transversity correlations

• Need to go beyond inclusive hadrons

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

What makes the proton spin? – Carl Gagliardi 44 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 45 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 46 Mid-rapidity interference fragmentation functions

1.0

0.9 q+q --> q+q 0.8 q+g --> q+g or g+q q+q' --> q+q' or q'+q π+ π- IFF 0.7 0.6 0.5

D_TT 0.4 0.3 0.2 0.1 0.0 -1.0 -0.5 0.0 0.5 1.0 cos theta* π+ π- IFF

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

What makes the proton spin? – Carl Gagliardi 47 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 substantially over the next few years. Stay tuned!

What makes the proton spin? – Carl Gagliardi 48