Research for the origin of generation of elementary particles based on supersymmetric grand unified theory

本研究的目的是阐明包含夸克、轻子和希格斯的超对称大统一理论作为非紧致水平对称性的无限维表象的唯象特征，并寻找其理论背景。大统一理论的一大主题是阐明自然实现质量比统一尺度轻得多的轻希格斯的机制。在这个理论中，希格斯通过理论的相结构，通过大统一对称性和水平对称性的自发破裂的关联，实现了希格斯是轻的。也就是说，作为希格斯内部伙伴的色三重态可以在不微调保留希格斯双重态光的情况下获得巨大的质量。为此，由于两个场属于相同的SU(1，1)表示但不同的SU(5)表示，必然存在自发对称性破缺。这两个场的真空期望值之比r决定了理论的手征粒子谱作为相结构。只有希格斯双重态才能手征实现，这个比率r必须小于1。此外，这个比率r重现了夸克和轻子与希格斯的Yukawa耦合矩阵中r的幂的层次结构。由SU(1，1)确定的数值因子通过对角化显著地扩大了本征值(质量)的等级。大统一理论的两种层级的大问题是通过水平对称性的自发破缺而被统一理解的。在这个理论中，中微子获得质量的机制不同于众所周知的跷跷板机制。最大的元素是非对角线的2-3代元素，从而实现了u-中微子和tau-中微子的最大混合。

The purpose of this research is to clarify the phenomenological feature of the supersymmetric grand unified theory containing quarks, leptons and Higgses as the infinite dimensional representation of noncompact horizontal symmetry, and search for its theoretical background. The big subject of the grand unified theory is to clarify the mechanism which naturally realizes light Higgs with mass much lighter than unification scale. In this theory, Higgs is realized to be light through phase structure of the theory by the correlation of the spontaneous breakdown of grand unified symmetry and horizontal symmetry. That is, color triplet, which is the GUT partner of Higgs, can obtain huge mass without fine tuning retaining Higgs doublet light. For this, there must be spontaneous symmetry breaking due to two fields which belong to the same SU(1,1) representation but different SU(5) representations. The ratio r of the vacuum expectation values of these two fields determins the chiral particle spectrum of the theory as the phase structure. In order only for the Higgs doublet to be realized chirally, this ratio r must be less than 1. Furthermore, this ratio r reproduces the hierarchical structure in power of r in the Yukawa coupling matrix of quarks and leptons with Higgs. The numerical factor determined by SU(1,1) remarkably enlarges, through diagonalization, the hierarchy of eigenvalues (masses). The big problems of two types of Hierarchies of grand unified theory are understood in a unified manner through spontaneous breakdown of horizontal symmetry. In this theory, neutrinos acquire masses through mechanism different from well-known seesaw mechanism. The largest element is off-diagonal 2-3 generation element, and therefore the maximal mixing between mu-nutrino and tau-nutrino is realized.