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Spin structure of the nucleon reflects
non-perturbative physics in QCD
Natural questions are what carries the rest of
the nucleon spin?
In this thesis, we study the GPDs using the
light-cone wave function based on the chiral
quark soliton model (CQSM)
In QCD, the candidates for the missing spin
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Why light-cone wave function ?
High energy observable (GPDs, parton distribution)
Non-local quark operator
In the light-cone frame
Quark (anti-quark) number operator
Light-cone wave function
Partonic interpretation very clear
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QCD definitions of the GPDs
Deeply virtual Compton scattering
Soft part including non-perturbative
information
GPD
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Light-cone coordinate

• Spin unpolarized case

• Spin polarized case

longitudinal momentum transfer
Squared momentum transfer
Feynman variable
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Properties of the GPDs

• Forward limit

momentum space distribution

• x moments of GPDs

coordinate space distribution
GPDs provide totally new information on baryon
structure
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Jis sum rule
Total quark contribution can be decomposed
gauge invariantly into the quark spin and
orbital contribution
Knowing and , one can extract the
quark orbital angular momentum
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Partonic interpretation of GPD
Dirac field
quark (anti-quark) creation and annihilation
operators

• Three kinematical regions

Quark distribution
Meson distribution amplitude
Antiquark distribution
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Overlap representation

• Fock state decomposition

Non-diagonal matrix element
(Meson distribution amplitude)
Need for the theory which can deal with the
higher Fock component
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Light-cone wave function in the CQSM
Basic lagrangian
Effective action

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3 valence quarks
Indefinite number of quark and anti-quark pairs
Deep Dirac sea
Distorted Dirac sea continuum
Fourier transform of equal time quark Green
function
quark
anti-quark
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Baryon w.f. is given by the product of valence
part and coherent exponential of quark
anti-quark pair
valence quark w.f.
Dirac sea continuum w.f.
w.f. in the Infinite Momentum Frame (IMF)
Light-cone w.f.
Lorentz boost
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Light-cone wave function representation of
the GPDs in the CQSM

• Normalization

we take up to 5Q components in the w.f.
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• Physical observable

Matrix elements of some operators sandwiched
between the initial and the final wave functions
unpolarized case
polarized case

• 3q contribution to GPDs

unpolarized case
polarized case
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5Q contributions to GPDs

• valence part

Quark antiquark pair
3 valence quark
initial
final
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5Q contributions to GPDs

• Dirac sea quark part

quark contribution
antiquark contribution
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Non-diagonal Fock components contribution
Final representation
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Numerical results for GPDs
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zero momentum transverse case

• spin unpolarized u quark distribution

• spin polarized u quark distribution

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Impact parameter space parton distribution
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Impact parameter space parton distribution
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Large spatial distribution in the low x region
the pion cloud surrounding the three valence
quark core
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Summary and conclusions

• Light-cone wave function based on the CQSM

3 valence quarks coherent exponential of quark
anti-quark pair

• We have derived the light-cone w.f.
  representations
• for the GPDs based on the CQSM

• GPDs

region
Non-diagonal matrix elements in Fock space

• Discontinuity at

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With phase conventions of the Brodsky-Lepage
light-cone spinors

• Light-cone helicity non-flip part

• Light-cone helicity flip part

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• Valence quark wave function

h(p) upper component j(p) lower component

• Wave function of the Dirac continuum

quark
anti-quark
mean chiral fields
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Forward limit
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• asymmetry

NMC measurement
pion cloud effects
Dirac sea polarization
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• NuTeV anomaly

NuTeV group reported the value of the weak
mixing angle
prediction from standard model
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but
CQSM
Strange sea asymmetry explains nearly 70 of the
NuTeV anomaly
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Hedgehog ansatz
3 valence quarks
Deep Dirac sea
Soliton is not spin isospin eigenstate
Hedgehog
Projection method