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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!
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