Study of chiral symmetry and internal structure of the nucleon

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The purpose of this research is to extend our previous research on the internal structure of the nucleon based on the NJL model, examine the dynamical aspects of the model by calculating the structure function and study the change of the nucleon internal structure in nuclear medium. Since the light-cone formulation is the most convenient for calculating structure functions, we have developed the light-cone hamiltonian formalism of the NJL model. A characteristic feature of fermions on the light-cone is that the number of their dynamical components becomes half of the usual formulation and the elimination of the non-dynamical components in the presence of interactions is not trivial. We have introduced auxiliary fields corresponding to scalar and pseudo-scalar mesons to treat this problem. The constraint equations for the auxiliary fields are then solved with 1/N expansion, giving the gap equation in the lowest order and the interaction term in the hamiltonian in the next order. The pio … More n in this scheme is described by the Tamm-Dancoff equation for quark-antiquark system and the eigenfunction is directly related to the pion structure function. We have considered two regularization schemes to treat divergent integrals in the gap equation and the pion eigenvalue equation. One is an extended version of the scheme proposed by Lepage and Brodsky and is nearly equivalent to the regularization in the conventional formulation. The other is the one proposed by Lenz, Ohta, Thies and Yazaki and regularizes only the transverse directions while renormalizing the longitudinal direction in the way used for the Gross-Neveu model in the two dimentional world. The latter has been found to give much better results for the pion structure function. It is expected that this formalism will be a step towards a more general framework of describing the chiral symmetry on the light-cone. The nucleon structure function in the relativistic Faddeev approach has been also calculated with the light-cone variables though we have not yet developed the light-cone hamiltonian formalism in this case.In addition to the above, a relativistic harmonic oscillator quark model has been used to study the internal dynamics of a nucleon propagating in the nuclear medium in connection with the problem of color transparency. We have also investigated the interaction between H-dibaryons to examine the possibility of a multi-strangeness baryonic matter. Less