Probing the Fundamental Structure of the Nuclear Building ... · Probing the Fundamental Structure...
Transcript of Probing the Fundamental Structure of the Nuclear Building ... · Probing the Fundamental Structure...
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!