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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. 大西　陽一　　　（阪大）. 若松　正志　　　（阪大）. “Spin structure of the nucleon” reflects non-perturbative physics in QCD. Natural questions are what carries the rest of the nucleon spin?. Generalized parton distributions (GPDs) contain information of

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大西　陽一　　　（阪大）

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  1. ＱＣＤの有効模型に基づく光円錐波動関数を用いた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 大西　陽一　　　（阪大） 若松　正志　　　（阪大）

  2. “Spin structure of the nucleon” reflects non-perturbative physics in QCD Natural questions are what carries the rest of the nucleon spin? Generalized parton distributions (GPDs) contain information of the orbital angular momentum and 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

  3. 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

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

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

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

  7. Ji’s 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

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

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

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

  11. 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

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

  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 Quark antiquark pair 3 valence quark initial final

  16. 5Q contributions to GPDs Dirac sea quark part 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. represents a spatial density in the transverse directions and momentum density in the longitudinal direction Impact parameter space parton distribution

  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 • 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

  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 quark anti-quark mean chiral fields

  26. Forward limit

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

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

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

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