Transcript Outline  Introductory Remarks  Major areas of nucleon structure investigations with 12 GeV upgrade  Conclusion.

Outline
 Introductory Remarks
 Major areas of nucleon structure
investigations with 12 GeV upgrade
 Conclusion
Introduction
 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 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
 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 GeV Kinematic Coverage
Three Major Areas of Nucleon Structure
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:
3D Quark and Gluon Structure
of the Nucleon
GPDs
 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
P ' | J ( x) P  P ' |  J ( x)dx P : form factors
 P | J ( x) P : parton distribution
J(x): bilocal quark operator along light-cone
A Cartoon for the GPD
x1P
x2P'
x 
1 
x 
x2 
1 
x1 
P'
P
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)
Physical Meaning of GPDs at ξ=0
 Form factors can be related to charge densities in
the 2D transverse plane in the infinite-momentum
frame
b
y
bx
 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!
Mixed Coordinate and Momentum “3D” Picture
 Longitudinal Feynman momentum x
+ Transverse-plane coordinates b = (bx,by)
b
A 3D nucleon
Tomographic Pictures From Slicing the xCoordinates (Burkardt)
x
0.1
by
0.3
bx
0.5
up
down
Physical meaning of GPDs: Wigner 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
O ( x, p )   dxdpO ( x, p )W ( x, p )
Short of measuring the wave function, the Wigner function
contains the most complete (one-body) info about a quantum system.
Simple Harmonic Oscillator
N=0
Husimi distribution: positive definite!
N=5
Quark 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 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 Feynman-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
by
bx
How to Measure GPDs
 Deep exclusive processes:
Deeply-virtual
Compton scattering
Deeply-exclusive meson
production
What 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 (also V. 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
ep
epg
E = 11 GeV
L = 2x1035
T = 1000 hrs
DQ2 = 1 GeV2
Dx = 0.05
Selected
Kinematics
CLAS12 - DVCS/BH Target Asymmetry
Selected Kinematics
E = 11 GeV
Longitudinal polarized target
L = 1x1035
T = 1000 hrs
DQ2 = 1GeV2
Dx = 0.05
Spin-dependent DVCS Cross Section
Leading twist
Twist-3/Twist-2
Rho production to measure the fraction of quark
angular momentum
From 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 Factors
 The first moments of GPDs are related to
electroweak form factors.
 Compton form factors
Measurable from large
angle Compton scattering
Why one needs high-t form factors
 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 GeV upgrade
Neutron and Pion Form Factors
Testing pQCD calculations
Nucleon-Delta Transition From Factors
Compton form factor at 12 GeV
A Comprehensive Study of the
Nucleon Spin Structure
(see also Avakian’s talk)
Spin 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 Scattering
 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
Quantum Phase-Space Distributions of Quarks
Wpu(x,kT,r) “Mother” Wigner distributions
Probability to find a quark u in a
nucleon P with a certain polarization
in a position r and momentum k
GPD
TMD PDFs: fpu(x,kT),…
Measure momentum
transfer to quark
Direct info about
momentum distributions
GPDs: Hpu(x,,t), …
PDFs fpu(x),…
Form Factors
F1pu(t),F2pu(t )..
Measure momentum
transfer to target
Direct info about
spatial distributions
Inclusive measurement: g2 structure function
Inclusive Measurements: Quark helicity at large x
A Definitive Investigation of
Quarks at Highest x, Resonances,
Duality and Higher twists
Parton 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 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
f ( x)  H ( p,  )2 J L ( p,  ) J R ( p,  )S ((1  x) p,  )
 Total di-quark helicity zero.
Rnp 3/7
Ap & An -> 1.
Why is large-x perturbative? Example: Pion
 Leading-order diagram contributing to parton
distribution at large x
Farrar & Jackson
As x->1, the virtuality of
these lines goes to infinity
On-shell quark with longitudinal
momentum 1-x
Lattice 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
1
1
0.8
Weighting
in forming
moments
0.6
x
0.4
x2
x5
x3x4
0.2
0
0
0
0.2
0.4
0.6
0.6
0.8
1
1
Large-x Distributions are hard to access
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 Do
 Tag neutron through measuring spectator proton
 DIS from A=3 mirror nuclei
Duality 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
 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 from Duality
 Examples
Duality allows precise extraction of higher-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.
Conclusion
 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!