Study of chiral symmetry and internal structure of the nucleon

本研究的目的是扩展前人基于NJL模型对核子内部结构的研究，通过计算结构函数来考察模型的动力学方面，研究核子内部结构在核介质中的变化。由于光锥公式是最方便的计算结构函数，我们发展了NJL模型的光锥哈密顿形式。光锥上费米子的一个特征是它们的动力分量的数量变成通常公式的一半，并且在相互作用的存在下消除非动力分量不是微不足道的。我们引入了对应于标量和伪标量介子的辅助场来处理这个问题。然后对辅助场的约束方程进行1/N展开，得到最低阶的间隙方程和下一阶的哈密顿量中的相互作用项。该方案中的π介子结构用夸克-反夸克系统的tam - dancoff方程描述，其本征函数与介子结构函数直接相关。我们考虑了两种正则化方案来处理间隙方程和介子本征值方程中的发散积分。一种是由Lepage和Brodsky提出的方案的扩展版本，几乎等同于常规公式中的正则化。另一种是由Lenz， Ohta， Thies和Yazaki提出的，它只对横向进行正则化，而对纵向进行重新正则化，就像二维世界中的Gross-Neveu模型一样。发现后者对介子结构函数给出了更好的结果。我们期望这种形式将是向描述光锥上手性对称性的更一般框架迈出的一步。相对论Faddeev方法中的核子结构函数也用光锥变量进行了计算，尽管在这种情况下我们还没有发展出光锥哈密顿形式。此外，本文还利用相对论性谐振子夸克模型研究了核子在核介质中传播的内部动力学，并讨论了颜色透明度问题。我们还研究了h -重子之间的相互作用，以检验多重奇异重子物质的可能性。少

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