Study of Gauge-Yukawa Unified Model

初级粒子物理的理论工作的实质是理解当今的树参数，即标准模型(SM)，就几个基本参数而言。减少参数数量的传统方法是假设世界更加对称。沿着这条线值得庆祝的例子是大统一理论(GUTS)的想法，它的规范部门为我们提供了一个可检验的预测，其中一个低能规范耦合。直觉思想的自然延伸是将一种理论的规范和汤川遥菜联系起来。在本研究中，我们研究了利用耦合约化和有限性原理实现规范-汤川统一(GYU)的超对称腔。本研究的主要结果如下：1)根据最近的实验数据，我们证明了在第三代中用GYU构造超对称腔来预测底夸克和顶夸克质量是可能的。这意味着…在这些模型中可以解释更多的自上而下的层次，就像假设在肠道尺度上存在统一的规范对称性一样，可以解释SM的规范耦合的层次。2)我们用陀螺仪考察了不同的陀螺，发现汤川耦合中存在等值的顶部质量线，因此同一条线上的两个不同的陀螺仪模型不能仅用陀螺的顶部质量M_t来区分。如果它们位于不同的线上，则可以用M_t(IR)来区分它们。3)考虑了将软超对称破缺(SSB)扇区引入到GYU程序中，发现在具有GYU的软破缺超对称腔中，存在具有普适性的软超对称破缺参数的RG不变求和规则。此外，我们还发现这一普适求和规则在一大类四维超弦模型中也是成立的。由此，我们预计超对称内脏与GYU模型和超弦模型之间将会有密切的联系，我们希望沿着这条线的进一步研究将会对基本粒子相互作用的理论本质产生更深层次的理解。较少

The essence of theoretical efforts in Elementary Particle Physics is to understand the present day tree parameters the Standard Model (SM) in terms of a few fundamental ones. The traditional way of reducing the number of parameters is to assume that the world is more symmetric. Acelebrated example along this line is the idea of Grand Unified Theories (GUTs), whose gauge sector provided us with a testable prediction for one of the low energy gauge couplings. A natural extension of the GUT idea is to relate the gauge and Yukawa sectors of a theory. In the present research we investigated supersymmetric GUTs in which the Gauge-Yukawa Unification (GYU) is achieved using the principles of reduction of couplings and finiteness. The main results of the present study are the following :1) We showed that it is possible to construct supersymmetric GUTs with GYU in the third generation that can predict the bottom and top quark masses in accordance with the recent experimental data. This means tha … More t the top-bottom hierarchy could be explained in these models, in a similar way as the hierarchy of the gauge couplings of the SM can be explained if one assumes the existence of a unifying gauge symmetry at the GUT scale. 2) We investigated different GUTs with GYU.It is found that there are equiv-top-mass-lines in the Yukawa couplings so that two different GYU models on the same line cannot be distinguished by the top mass M_t alone. If they are on different lines, they could be distinguished by M_t (IR). 3) We considered the inclusion of the soft supersymmetry-breaking (SSB) sector into the program of GYU,and found that there exists in softly-broken supersymmetric GUTs with GYU a RG invariant sum rule of the SSB parameters that is universal in character. We, moreover, found that this universal sum rule is also satisfied in a wide class of four-dimensional superstring models.From these result we expect that there will be a close connection between supersymmeteric GUTs with GYU and superstring models, and we hope that further investigations along this line might yield deeper understandings of the theoretical nature of the interactions of the elementary particles. Less