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“Overview” of Nucleon Spin Structure
Xiangdong JiUniversity of Maryland
Workshop on Future Prospects on QCD at High-Enegy, BNL, July 19, 2006
Outline
Introduction Quark sea polarization Gluon polarization Orbital angular momentum and
generalized parton distribution Transverse spin physics Conclusion
Introduction
The driving force behind the modern cosmology is
The origin of energy density in the universe
Introduction
The driving force for high-energy spin physics is
Spin budget of the proton
25%
75%
Total proton spin = 1/2
Quark spin measuredin inclusive pol. DIS
“Dark” angular momentum?
Spin of the proton in QCD
The spin of the nucleon can be decomposed into contributions from quarks and gluons
Further decomposition of the quark contribution
Further decomposition of the gluon contribution
1/ 2 ( ) ( )q gJ J J
1[ ( ) ]2
v sq f f qf
f
J q q L
g gJ g L
gauge invariant
parton-physicsmotivated
Probing “dark” angular momentum
Quark-sea polarization HERMES semi-inclusive DIS Polarized RHIC & EIC
Gluon polarization COMPASS/HERMES semi-inclusive DIS Polarized RHIC & EIC
Quark orbital angular momentum Proton tomography HERMES, JLab, COMPASS, & EIC
Sea quark Polarization
The sea quark contribution: an indirect approach using SU(3) flavor symmetry
Quark spin contribution to the proton spin can be determined from the axial charges.
The isovector axial charge (neutron decay const.)
The octet axial charge (hyperon β-decays)
Inclusive polarized DIS yields
Together, they produce
1.257Au d g
2 0.585 0.025u d s
0.21 0.06u d s
0.09 0.02s Explains “spin crisis?”
Measuring the sea quark spin in SIDIS:
One can measure the sea quark contribution to the spin of the proton through fragmentation of the polarized quark into mesons (Close & Milner)
A major motivation for HERMES
HERMES resultAirapetian et al, PRL 92 (2004) 012005
Sea quark polarization
The result for s is very different from the inclusive DISplus SU(3) symmetry analysis!
Precision?Small x?QCD Factorization?SU(3) flavor symmetry?
Future possibilities
Polarized RHIC Can measure through W
boson production of polarized proton-proton collision at RHIC
Center of mass energy must be high
Neutrino elastic scattering Measuring the axial form
factor in elastic scattering
Parity Violating Structure Functions g5
Unique measurement with EIC
Experimental Signature: missing (neutrino) momentum: huge asymmetry in detector
Complementary measurement to RHIC SPIN
For EIC kinematics
Measurement Accuracy PV g5 with EIC
Assume:1) Input GS Polarized PDFs2) xF3 is measured well by that time3) 4fb-1 luminosity
If e+ and e- possible then one can have g5(+) as well.
Separate flavors u, d etc.
Flavor decomposition
EIC White Paper 2002 @1033 luminosity
(Stoesslein, Kinney)
Small x!
Gluon polarization g
Gluon polarization
Thought to be large because of the possible role of axial anomaly –(αs/2)g (Altarelli & Ross, 1988) 2-4 units of hbar!
Of course, the gluon contribute the proton spin directly.
1/2 = g + … One of the main motivations for COMPASS
and RHIC spin experiments! Surprisingly-rapid progress, but the error
bars remain large.
Experimental progress-I
Two leading-hadron production in semi-inclusive DIS
Q-evolution in inclusive spin structure function g1(x)
Experimental progress-II
production in polarized PP collision at RHIC
Two jet production in polarized PP collision at RHIC
Fit to data
g = 0.31 ± 0.32 type-1 = 0.47 ± 1.0 type-2
= —0.56 ± 2.16 type-3
Type-3 fit assumes gluon polarizationis negative at smallx.
Hirai, Kumano,Saito, hep-ph/003213
Theoretical prejudices
It shall be positive: There was a calculation by Jaffe (PRB365, 1996), showing
a negative result in NR quark and bag models. However, there are two type of contributions
The contribution calculated by Jaffe is cancelled by the one-body contribution.
Calculating x-dependence is in progress (P.Y. Chen)
Barone et al., PRB431,1998
Theoretical prejudices
It shall not be as large! The anomaly argument for large Δg is controversial
There is also an anomaly contribution to the quark orbital motion.
It is un-natural for heavy quarks.
Naturalness
Δq + Δg + Lz = 1/2 if Δg is very large, there must be a large negative Lz to
cancel this---(fine tuning!) Model predictions are around 0.5 hbar.
More data from RHIC
More precise measurement on pi production asymmetry
as well as two-jet production
Direct photon production, proportional to g linearly
STAR-jet
Gluon Distributions at EIC
Deep Inelastic Scattering Kinematics with EIC: Perturbative QCD analysis of the g1 spin structure of the
data 2+1 Jet production in photon gluon fusion (PGF) process 2-high pT opposite charged hadron tracks (PGF)
Photo-production (real-photon) Kinematics with EIC: Single jet production in PGF Di-Jet production in PGF Open charm production
G(x)/G(x) EIC vs. Rest of the World
EIC Di-Jet DATA 2fb-1
Good precisionClean measurementRange 0.01 <x< 0.3Constrains shape!!
g1(x) at small x
Orbital angular momentum
Argument for large orbital motion
Quarks are essentially massless. A relativistic quark moving in a small region of space must have non-zero orbital angular momentum. (MIT bag model)
Finite orbital angular momentum is essential for Magnetic moment of the proton. g2 structure function Asymmetric momentum-dependent parton distribution
in a transversely polarized nucleon …
OAM and Wigner distribution
To measure orbital motion, one must have information of a parton’s position and momentum simultaneously.
A natural observable is the so-called Wigner distribution in Quantum Mechanics.
When integrated over x (p), one gets the momentum (probability) density.
Not positive definite in general (not strict density), but is in classical limit!
Any dynamical variable can be calculated as
),(),(),( pxWpxdxdpOpxO
Harmonic oscillator & squeezed light
n=0
Wiger distribution or squeezed light!
n=5
Generalized parton distributions
Off-forward matrix elements
Reduces to ordinary parton distribution when t->0 x-moments yield electromagnetic, gravitational,…etc
form factors
P P'
x1P x2P'
)(
2/)(
)'(
21
21
2
xx
xxx
ppt
3D images of quarks at fixed-x
GPDs as Wigner distribution can be used to picture quarks in the proton (A. Belitsky, X. Ji, and F. Yuan, PRD, 2004) The associated Winger distribution is a function of position
r and Feynman momentum x: f(r,x) One can plot the Wigner distribution as a 3D function at
fixed x A GPD model satisfying known constraint:
x
y
z
Integrating over z 2D Impact parameter space
Th. Feldman
Total quark angular momentum
The total angular momentum is related to the GPDs by the following sum rule
Where E and H are GPDs defined for unpolarized quarks.
In the forward limit, H reduces to ordinary parton distribution q(x).
E can best be determined with a trans. pol. target.
0
1lim [ ( , , ) ( , , )]
2q q qtJ dxx H x t E x t
Measuring GPD
Deeply virtual Compton scattering
Deeply virtual meson production (replacing the photon by mesons)
Measurements have been made at HERA & Jlab:
DVCS with transversely polarized target
Looking forward
Jlab 12 GeV upgradeA comprehensive program to study GPDs
HERMES & COMPASS : rho production on transversely polarized target
Vanderhaeghen et al.
Deeply Virtual Compton Scattering at EICD. Hasell, R. Milner et al.
EIC: 5 GeV e on 50 GeV proton:
Could be measured with EIC with considerable x,Q2 range.
DVCS at EIC (preliminary)
10 x 250 GeV
Q2> 1 GeV2
20<W<95 GeV0.1<|t|<1.0 GeV2
Full curve: all eventsDashed curve: accepted events Q2>1 GeV2: 50K events/fb-1
A. Sandacz
Acceptance enhancedZEUS-like detector Add Roman pots a la PP2PP at RHIC
Transverse Spin Physics
left
right
Driving questions
What effects can transverse spin produce in a high-energy collision process?
What can one learn about the quark-gluon structure of the proton form these effects? Transversity distribution Quark-gluon correlations TMD quark distributions
)()(
)()(
LTA
Transverse spin asymmetries
pp ep
ep e+e-
Understanding the Asymmetries
If a process does not involve hard momentum transfer, our understanding is very limited. pp: SSA at small transverse momentum ep: spin asymmetry at small Q2
Hard processes: either a large transverse-momentum or a high Q QCD factorization theorems Asymmetries are related to underlying parton
properties: i.e. parton distributions & fragmentations
Observable Asymmetries
Single Spin Asymmetries pp to semi-inclusive hadrons (twist-3) pp to *, W, Z + X, small P (twist-2) pp to 2 jets, jet+ , small P (twist-2) ep to semi-inclusive hadrons, small P (twist-2)
Double Spin Asymmetries pp to *, W, Z + X (twist-2) pp to jets, heavy quarks (twist-2) ep inclusive g2 (twist-3) ep to polarized + X (twist-2) ep to semi-inclusive two hadrons (twist-2)
Angular Correlation: e+e- to hh’ + X (twist-2)
Transverse-Spin Related Distributions
Transversity Distribution q(x) or h(x) (twist-2) the density of transversely polarized quarks in a transversely
polarized nucleon chirally-odd
Sivers function qT(x, k) (twist-2 at small k) Asymmetric distribution of quarks with T-momentum k in a
transversely polarized nucleon T-odd, depends on ISI/FSI
Twist-3 Quark-gluon correlation functions Polarized gluons!
Related Fragmentation functions
A unified picture for SSA
In DIS and Drell-Yan processes, SSA depends on Q and transverse-momentum P
At large P, SSA is dominated by twist-3 correlation effects (Afremov& Teryaev, Qiu & Sterman)
At moderate P, SSA is dominated by the k-dependent parton distribution/fragmentation functions
Ji, Qiu, Vogelsang, & Yuan (2006) The two mechanisms at intermediate P
generate the same physics!
What have we learned from data?
SSA in PP scattering is large, even at RHIC energy. Consistent with twist-3 expectation.
SSA in eP scattering is large at HERMES, becomes smaller at COMPASS. The Collins function is
consistent with e+e- data, but with very striking charge behavior
Siver’s function has striking flavor dependence
Future Challenge?
PQCD & Factorization? Is P =1-2 GeV high enough to use pQCD ? (a twist-3 effect,
scaling, maybe ok for total cross section.) Is the perculiar flavor dependence in HERMES data due to
non-perturbative physics? Or non-precise data? (g2)
Transverse-spin effort small at large energy? Jaffe & Saito, QCD selection rule (1996) Vogelsang & others, small ATT asymmetry for Drell-Yan PAX collaboration at GSI, PP-bar scattering at lower energy
The ultimate goal? Can one measure transversity to a good precision? Can one calculate TMD & Twist-3 correlations?
EIC with transverse spin
Angular MomentumTransversity
Conclusion
The proton spin structure is a fundamental question in QCD.
Much work is need to identify the “dark” angular momentum!
The field is active with COMPASS, Polarized RHIC underway Jlab 12 GeV on the horizon
EIC can definitive contributions to all aspects of proton spin physics, and bring the field to its maturity.
Spin budget of the proton
Spin budget of the proton
25%
75%
Quark spin
?
Total proton spin = 1/2