Probing the Fundamental Structure Probing the Fundamental Structure of the Nuclear Building Blocks with of the Nuclear Building Blocks with

JlabJlab 12 12 GeVGeV UpgradeUpgrade

Xiangdong JiUniversity of Maryland

— Jlab 12 GeV upgrade review, Jan. 10, 2005

OutlineOutline

Introductory RemarksMajor areas of nucleon structure investigations with 12 GeV upgradeConclusion

IntroductionIntroduction

Nucleons are the basic building blocks of atomic nuclei. Their internal structure, arising from the underlying quark and gluon constituents, determines their mass, spin, and interactions.These, in turn, determine the fundamental properties of the nuclei and atoms.Nucleon physics represents one of the most important frontiers in modern nuclear physics.

The Two Traditional ObservablesThe Two Traditional Observables

Elastic Form Factors– Low Q: charge and current distributions.

High Q: light-cone parton distribution amplitudes, underlying pQCD reaction mechanism,

– Starting from Hofstadter’s work in 1950’s– Well-measured for some, not so for others

• Neutron form factors• Large Q2

• …

The Two Traditional Observables The Two Traditional Observables

Feynman Parton Distributions– Distributions of quarks in momentum space.– Starting from Freedman, Kendall and Taylor’s DIS

experiments at SLAC– Well-measured in some kinematics. But some key

aspects are missing• Parton distributions as x 1• Spin-flavor dependence• …

12 12 GeVGeV KinematicKinematic CoverageCoverage

Three Major Areas of Nucleon Structure Three Major Areas of Nucleon Structure Studies With 12 Studies With 12 GeVGeV

1. Major New Direction: 3D mapping of the quark structure of the nucleon

2. Comprehensive Study of nucleon spin structure (also Avakian’s talk)

3. Definitive Investigation of quarks at highest x, resonances, duality, and higher twists.

A Major New Direction:A Major New Direction:3D Quark and Gluon Structure 3D Quark and Gluon Structure

of the Nucleonof the Nucleon

GPDsGPDs

Detailed mapping of the structure of the nucleon using the

Generalized Parton Distributions (GPDs)

A proton matrix element which is a hybrid of elastic form factor and Feynman distribution

' | ( ) ' | ( ) : form factors

| ( ) : parton distribution

P J x P P J x dx P

P J x P

→

→

∫

J(x): bilocal quark operator along light-cone

A Cartoon for the GPDA Cartoon for the GPD

x: average fraction of the longitudinal momentum carried by parton, just like in the Feynman parton dis.

t=(p’-p)2: t-channel momentum transfer squared, like in form factor

ξ: skewness parameter ~ x1-x2

Recent Review: M. Diehl, Phys. Rep. 388, 41 (2003)

P P'

x1P x2P' 1

2

1

1

xx

xx

ξξξξ

−=

−+

=+

Physical Meaning of Physical Meaning of GPDsGPDs at at ξξ=0=0

Form factors can be related to charge densities in the 2D transverse plane in the infinite-momentum frame

Feynman parton distribution is a quark density in the longitudinal momentum x, The Fourier transformation of a GPD H(x,t, ξ=0) give the density of quarks in the “combined” 2+1 space!

bx

by

Mixed Coordinate and Momentum “3D” PictureMixed Coordinate and Momentum “3D” Picture

Longitudinal Feynman momentum x+ Transverse-plane coordinates b = (bx,by)

b

A 3D nucleon

TomographicTomographic Pictures From Slicing the xPictures From Slicing the x--Coordinates (Coordinates (BurkardtBurkardt))

x

bx

by

up down

0.1

0.3

0.5

Physical meaning of Physical meaning of GPDsGPDs: : WignerWigner functionfunction

For one-dim quantum system, Wigner function is

– When integrated over x (p), one gets the momentum (probability) density.

– Not positive definite in general, but is in classical limit.– Any dynamical variable can be calculated as

∫= ),(),(),( pxWpxdxdpOpxO

Short of measuring the wave function, the Wigner functioncontains the most complete (one-body) info about a quantum system.

Simple Harmonic OscillatorSimple Harmonic Oscillator

N=5N=0

HusimiHusimi distribution: positive definite!distribution: positive definite!

Quark Quark WignerWigner DistributionsDistributions

Functions of quark position r, and its Feynman momentum x.Related to generalized parton distributions through

t= – q2

ξ ~ qz

PhasePhase--Space Charge Density and Current Space Charge Density and Current

Quark charge density at fixed Feynman x

Quark current at fixed Feynman x in a spinning nucleon (spinning around the spatial x-direction)

* Quark angular momentum sum rule:

Imaging quarks at fixed FeynmanImaging quarks at fixed Feynman--xx

For every choice of x, one can use the Wignerdistributions to picture the nucleon in 3-space; This is analogous to viewing the proton through the x (momentum) filters!

z

bybx

How to Measure How to Measure GPDsGPDs

Deep exclusive processes:

Deeply-virtual Compton scattering

Deeply-exclusive meson production

What 12 What 12 GeVGeV can docan do

The first machine in the world capable of studying these novel exclusive processes in a comprehensive way– High luminosity! – Large acceptance!

What do we need?small t, large x-range, high Q2

12 GeV upgrade will deliver these!

What one can measure What one can measure (also V. (also V. Burkert’sBurkert’s talk)talk)

Beam spin asymmetry, longitudinal and transverse single target-spin asymmetries for DVCS and meson production(measuring imaginary part of the amplitudes, x= ξ)Separation of different GPDs(E, H, H-tilde, etc.)

Absolute cross section measurements (get real part of Compton amplitude (principal value))Exploration of double DVCS process to map x and ξ independently.…

CLAS12 - DVCS/BH Beam Asymmetry

e p epγ E = 11 GeV

L = 2x1035

T = 1000 hrs∆Q2 = 1 GeV2

∆x = 0.05

Selected Kinematics

CLAS12 - DVCS/BH Target Asymmetry

E = 11 GeVSelected Kinematics

Longitudinal polarized targetL = 1x1035

T = 1000 hrs∆Q2 = 1GeV2

∆x = 0.05

SpinSpin--dependent DVCS Cross Sectiondependent DVCS Cross Section

Leading twist

Twist-3/Twist-2

RhoRho production to measure the fraction of quark production to measure the fraction of quark angular momentumangular momentum

From observables to From observables to GPDsGPDs

Direct extraction GPDs from cross sections and asymmetries at certain kinematics.Global fits with parameterizations.Partial wave analysis (expand in a certain basis)Lattice QCD calculations can provide additional constraints.Effective field theory (large Nc and chiraldynamics) constraintsPhenomenological models

GPD Constraints from Form FactorsGPD Constraints from Form Factors

The first moments of GPDs are related to electroweak form factors.

Compton form factors

Measurable from largeangle Compton scattering

Why one needs highWhy one needs high--t form factorst form factors

High resolution for quark distributions in impact parameter spaceTesting pQCD predictions, – helicity conservation– mechanisms for high-t reactions

(soft vs. hard reaction mechanisms)12 GeV capabilities– proton charge FF ~ 14 GeV2

– neutron magnetic FF ~ 14 GeV2

– neutron electric FF ~ 8 GeV2

– Compton FF: s ~ 20 GeV2, t ~ 17 GeV2

Proton Form Factors with 12 Proton Form Factors with 12 GeVGeV upgradeupgrade

Neutron and Neutron and PionPion Form FactorsForm Factors

Testing pQCD calculations

NucleonNucleon--Delta Transition From FactorsDelta Transition From Factors

Compton form factor at 12 Compton form factor at 12 GeVGeV

A Comprehensive Study of the A Comprehensive Study of the Nucleon Spin StructureNucleon Spin Structure

(see also Avakian’s talk)

Spin Structure of the NucleonSpin Structure of the Nucleon

The spin was thought to be carried by the spin of the three valence quarksPolarized deep-inelastic scattering found that only 20-30% are in these.A host of new questions:– Flavor-dependence in quark helicity distributions?

Polarization in sea quarks?– Transversity distributions? – Transverse-momentum-dependent (TMD) parton

distributions (Single spin asymmetry and T-odd distributions, Collins and Sivers functions)

– Orbital angular momentum of the quarks?

SemiSemi--Inclusive Deep Inelastic ScatteringInclusive Deep Inelastic Scattering

Has been explored at Hermes and other exptswith limited statisticsJlab 12 GeV could make the definitive contribution! (Avakian’s talk)

– Measuring mostly meson (pion, kaon) production • longitudinal momentum fraction z• transverse momentum p⊥ ~ few hundred MeV

TMD parton distributions

TMD PDFs: fpu(x,kT),…

d 2kT

ξ=0,t

=0

dx

Wpu(x,kT,r) “Mother” Wigner distributions

d3r d 2k

T

Quantum Phase-Space Distributions of Quarks

Measure momentum transfer to targetDirect info about spatial distributions

Measure momentum transfer to quarkDirect info about momentum distributions

GPD

Probability to find a quark u in a nucleon P with a certain polarization in a position r and momentum k

(FT)

GPDs: Hpu(x,ξ,t), …

Form Factors F1p

u(t),F2pu(t )..

PDFs fpu(x),…

Inclusive measurement: gInclusive measurement: g22 structure functionstructure function

Inclusive Measurements: Quark Inclusive Measurements: Quark helicityhelicity at large xat large x

A Definitive Investigation of A Definitive Investigation of Quarks at Highest x, Resonances, Quarks at Highest x, Resonances,

Duality and Higher twistsDuality and Higher twists

PartonParton Distributions at large xDistributions at large x

Large-x quark distribution directly probes the valence quark configurations.– Better described, we hope, by quark models.– Standard SU(6) spin-flavor symmetry predictions

• Rnp = Fn/Fp=2/3, Ap = g/F=5/9, An=0– Symmetry breaking (seen in parton distribution at x>0.4)

• One-gluon (or pion) exchange higher effective mass for vector diquark.Rnp = ¼, Ap=An = 1

• Instanton effects? Ap = – 1, An = 0

PerturbativePerturbative QCD prediction at large xQCD prediction at large x

Perturbative QCD prediction q(x) ~ (1-x)3 Farrar and Jackson, 1975

the coefficient, however, is infrared divergent!– The parton distribution at x 1 exhibits the following

factorization

Total di-quark helicity zero.Rnp 3/7Ap & An -> 1.

2( ) ( , ) ( , ) ( , ) ((1 ) , )L Rf x H p J p J p S x pµ µ µ µ= −

Why is largeWhy is large--x x perturbativeperturbative? Example: ? Example: PionPion

Leading-order diagram contributing to partondistribution at large x

OnOn--shell quark with longitudinal momentum 1-x

As As x->1, the virtuality of these lines goes to infinityFarrar & Jackson

Lattice QCD calculationsLattice QCD calculations

Parton structure of the nucleon can best be studied through first-principle, lattice QCD calculations of their moments. Mellin moments emphasize large x-partondistributions

1

0 0.2 0.4 0.6 0.8 1

0

0.2

0.4

0.6

0.8

1

xx2

x3x4x5

0 10.6

Weightingin forming moments

LargeLarge--x Distributions are hard to access x Distributions are hard to access experimentallyexperimentally

Low rates, because parton distributions fall quickly there – need high luminosity

No free neutron target:– Nuclear effects are

important at large xScaling? (duality)

What 12 What 12 GeVGeV Upgrade Can DoUpgrade Can Do

Tag neutron through measuring spectator protonDIS from A=3 mirror nuclei

Duality and ResonancesDuality and Resonances

As x->1 the scaling sets in later and later in Q, as the final-state invariant mass is

W2 = M2 + Q2(1-x)/x Resonance production is dominant!However, the resonance behaviors are not arbitrary. Taken together, they reflect, on an average sense, the physics of quark and gluons=> (global) parton-hadron duality.

Studied quantitatively at Jlab 6 GeV.

Extended exploration at 12 Extended exploration at 12 GeVGeV

What 12 GeV can do– Separation of L/T responses – Duality in spin observables?– Duality in semi-inclusive processes?What is duality good for?– Accessing the otherwise inaccessible

• Resonances partons, as in QCD sum rules, • Exploring limitations of QCD factorizations

– Studying quark-gluon correlations and higher-twists

PartonParton Distributions at large x from DualityDistributions at large x from Duality

Examples

Duality allows precise extraction of higherDuality allows precise extraction of higher--twiststwists

Higher-twist matrix elements encode quark-gluon correlations.They are related to the deviation of the average resonance properties from the parton physics, and mostly reside at large-x.Studies of resonances and duality allow precision extraction of higher-twist matrix elements.

ConclusionConclusion

The Jlab 12 GeV upgrade will support a great leap forward in our knowledge of hadronstructure through major programs in three areas:– Generalized parton distribution and 3D structure of

the nucleon.– Spin structure of the nucleon via semi-inclusive DIS

processes.– Parton, resonance, and duality physics at large-x.And

Let’s DO IT!Let’s DO IT!