OutlineOutline

Introductory Remarks

Major areas of nucleon structure investigations with 12 GeV upgrade

Conclusion

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 x1

• Spin-flavor dependence

• …

12 GeV Kinematic Coverage12 GeV Kinematic Coverage

Three Major Areas of Nucleon Three Major Areas of Nucleon Structure Studies With 12 GeVStructure Studies With 12 GeV

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 3D Quark and Gluon

Structure 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 inform 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

Physical Meaning of GPDs at Physical Meaning of GPDs 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 Mixed Coordinate and Momentum “3D” Picture“3D” Picture

Longitudinal Feynman momentum x

+ Transverse-plane coordinates b = (bx,by)

b

A 3D nucleon

Tomographic Pictures From Slicing Tomographic Pictures From Slicing the x-Coordinates (Burkardt)the x-Coordinates (Burkardt)

bx

by

up down

x

0.1

0.3

0.5

Physical meaning of GPDs: Physical meaning of GPDs: Wigner functionWigner function

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

Husimi distribution: positive definite!Husimi distribution: positive definite!

N=0 N=5

Quark Wigner DistributionsQuark Wigner Distributions

Functions of quark position r, and its Feynman momentum x.

Related to generalized parton distributions through

t= – q2

~ qz

Phase-Space Charge Density Phase-Space Charge Density and Current 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 Imaging quarks at fixed Feynman-xFeynman-x

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

z

bx

by

How to Measure GPDsHow to Measure GPDs

Deep exclusive processes:

Deeply-virtual Compton scattering

Deeply-exclusive meson production

What 12 GeV can doWhat 12 GeV can 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’s talk)Burkert’s 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 = 11 GeV

Selected Kinematics

L = 2x1035

T = 1000 hrsQ2 = 1 GeV2

x = 0.05

e p ep

L = 1x1035

T = 1000 hrsQ2 = 1GeV2

x = 0.05

CLAS12 - DVCS/BH Target Asymmetry

E = 11 GeVSelected Kinematics

Longitudinal polarized target

Spin-dependent DVCS Cross Spin-dependent DVCS Cross SectionSection

Leading twist

Twist-3/Twist-2

Rho production to measure the Rho production to measure the fraction of quark angular momentumfraction of quark angular momentum

From observables to GPDsFrom observables to GPDs

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 chiral dynamics) constraints

Phenomenological models

GPD Constraints from Form GPD Constraints from Form FactorsFactors

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

Compton form factors

Measurable from largeangle Compton scattering

Why one needs high-t form Why one needs high-t form factorsfactors

High resolution for quark distributions in impact parameter space

Testing 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 GeV upgradeGeV upgrade

Neutron and Pion Form FactorsNeutron and Pion Form Factors

Testing pQCD calculations

Nucleon-Delta Transition From Nucleon-Delta Transition From FactorsFactors

Compton form factor at 12 GeVCompton form factor at 12 GeV

A Comprehensive Study of A Comprehensive Study of the Nucleon Spin Structurethe Nucleon 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 quarks

Polarized 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?

Semi-Inclusive Deep Inelastic Semi-Inclusive Deep Inelastic ScatteringScattering

Has been explored at Hermes and other expts with limited statistics

Jlab 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

PDFs fpu(x),… Form Factors

F1pu(t),F2p

u(t )..

TMD PDFs: fpu(x,kT),…

d 2kT

=0,

t=0

dx

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

d3 r 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,,t), …

Inclusive measurement: gInclusive measurement: g22 structure structure functionfunction

Inclusive Measurements: Quark Inclusive Measurements: Quark helicity at large xhelicity at large x

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

Resonances, Resonances, Duality and Higher twistsDuality and Higher twists

Parton Distributions at large xParton Distributions 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

Perturbative QCD prediction at Perturbative QCD prediction at large xlarge x

Perturbative QCD prediction

q(x) ~ (1-x)3 Farrar and Jackson, 1975the coefficient, however, is infrared divergent!

– The parton distribution at x1 exhibits the following factorization

Total di-quark helicity zero.

Rnp 3/7

Ap & An -> 1.

2( ) ( , ) ( , ) ( , ) ((1 ) , )L Rf x H p J p J p S x p

Why is large-x perturbative? Why is large-x perturbative? Example: PionExample: Pion

Leading-order diagram contributing to parton distribution at large x

On-On-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-parton distributions

0 0.2 0.4 0.6 0.8 1

0

0.2

0.4

0.6

0.8

1

xx2

x3x4

x5

0 10.6

1

Weightingin forming moments

Large-x Distributions are hard to Large-x Distributions are hard to access experimentallyaccess experimentally

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

No free neutron target: – Nuclear effects are

important at large x

Scaling? (duality)

What 12 GeV Upgrade Can DoWhat 12 GeV Upgrade Can Do

Tag neutron through measuring spectator proton

DIS 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 GeV Extended exploration at 12 GeV

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

Parton Distributions at large x Parton Distributions at large x from Dualityfrom Duality

Examples

Duality allows precise extraction of Duality allows precise extraction of higher-twistshigher-twists

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 hadron structure 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!