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、轻子和希格斯粒子的超对称大统一理论作为非紧水平对称的无限维表象的唯象特征，并寻找其理论背景。大统一理论的大课题是阐明自然实现质量比统一尺度轻得多的轻希格斯粒子的机制。在该理论中，通过大统一对称性自发破缺与水平对称性的关联，通过该理论的相结构实现了Higgs的光化。也就是说，色三重态，这是大统一理论的合作伙伴的希格斯，可以获得巨大的质量没有微调保留希格斯二重态光。对于这一点，由于两个场属于相同的SU（1，1）表示，但不同的SU（5）表示，必须有自发的对称性破缺。这两个场的真空期望值之比r决定了作为相结构的手征粒子谱。为了使希格斯偶线能够手性地实现，这个比值r必须小于1。此外，这个比率r再现了夸克和轻子与希格斯粒子的汤川耦合矩阵中r次方的等级结构。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）的层次。大统一理论的两种层次的大问题是通过水平对称性的自发破缺来统一理解的。在这个理论中，中微子通过不同于众所周知的跷跷板机制的机制获得质量。最大的单元是非对角2-3代单元，因此实现了μ-nutrino和τ-nutrino之间的最大混合。

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.