“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