1. 大西 陽一 （阪 大） ＱＣＤの有効模型に基づく光円錐波動関数を用い た 一般化パートン分布関数の研究 若松 正志 （阪大）

2. In QCD, the candidates for the missing spin In this thesis, we study the GPDs using the light-cone wave function based on the chiral quark soliton model (CQSM) Generalized parton distributions (GPDs) contain information ofthe orbital angular momentum and “Spin structure of the nucleon” reflects non-perturbative physics in QCD Natural questions are what carries the rest of the nucleon spin?

3. Why light-cone wave function ? Non-local quark operator High energy observable (GPDs, parton distribution) In the light-cone frame Quark (anti-quark) number operator Light-cone wave function Partonic interpretation very clear

4. QCD definitions of the GPDs Deeply virtual Compton scattering Soft part including non-perturbative information GPD

5. Spin unpolarized case Spin polarized case Squared momentum transferFeynman variable longitudinal momentum transfer Light-cone coordinate

6. Properties of the GPDs Forward limit : x moments of GPDs momentum space distribution coordinate space distribution GPDs provide totally new information on baryon structure

7. Ji’s sum rule Knowing and, one can extract the quark orbital angular momentum Total quark contribution can be decomposed gauge invariantly into the quark spin and orbital contribution

8. Partonic interpretation of GPD Dirac field Three kinematical regions : quark (anti-quark) creation and annihilation operators Quark distribution Antiquark distribution Meson distribution amplitude

9. Overlap representation Fock state decomposition Non-diagonal matrix element Need for the theory which can deal with the higher Fock component (Meson distribution amplitude)

10. Light-cone wave function in the CQSM Effective action Dynamical quark mass M=375MeV Spontaneous chiral symmetry breaking of the QCD vacuum Strong coupling between pion and quark Basic lagrangian

11. 3 valence quarks Deep Dirac sea Indefinite number of quark and anti-quark pairs Distorted Dirac sea continuum : Fourier transform of equal time quark Green function quarkanti-quark

12. 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. Lorentz boost Light-cone w.f. w.f. in the Infinite Momentum Frame (IMF)

13. Light-cone wave function representation of the GPDs in the CQSM Normalization we take up to 5Q components in the w.f.

14. 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 :

15. 5Q contributions to GPDs valence part initialfinal Quark antiquark pair 3 valence quark

16. Dirac sea quark part 5Q contributions to GPDs quark contribution antiquark contribution

17. Non-diagonal Fock components contribution Final representation

18. Numerical results for GPDs

19. zero momentum transverse case : spin unpolarized u quark distribution spin polarized u quark distribution

20. Impact parameter space parton distribution represents a spatial density in the transverse directions and momentum density in the longitudinal direction

21. Impact parameter space parton distribution

22. Large spatial distribution in the low x region the pion cloud surrounding the three valence quark core

23. Summary and conclusions Light-cone wave function based on the CQSM 3 valence quarks + coherent exponential of quark anti-quark pair GPDs region Non-diagonal matrix elements in Fock space Discontinuity at We have derived the light-cone w.f. representations for the GPDs based on the CQSM

24. With phase conventions of the Brodsky-Lepage light-cone spinors Light-cone helicity non-flip part Light-cone helicity flip part

25. Valence quark wave function h(p) : upper component j(p) :lower component Wave function of the Dirac continuum mean chiral fields quarkanti-quark

26. Forward limit

27. asymmetry NMC measurement pion cloud effects Dirac sea polarization Gottfried sum

28. NuTeV anomaly NuTeV group reported the value of the weak mixing angle :prediction from standard model ? :CQSM but Strange sea asymmetry explains nearly 70% of the NuTeV anomaly

29. 3 valence quarks Deep Dirac sea Hedgehog ansatz Soliton is not spin isospin eigenstateHedgehog Projection method