Study of Gauge-Yukawa Unified Model

基本粒子物理学理论工作的本质是根据几个基本参数来理解标准模型（SM）中目前的三种参数。减少参数数量的传统方法是假设世界更加对称。沿着这条路线的一个著名的例子是大统一理论（GUTs）的思想，它的规范部门为我们提供了一个低能量规范耦合的可测试预测。GUT思想的自然延伸是将理论的规范扇区和汤川扇区联系起来。在本研究中，我们研究了利用耦合约化和有限性原理实现Gauge-Yukawa统一（GYU）的超对称大统一。本研究的主要结果如下：1)根据最近的实验数据，我们证明了用第三代GYU构造可以预测底夸克和顶夸克质量的超对称GUTs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结构，就像假设在GUT尺度上存在统一的规范对称，可以解释SM规范耦合的层次结构一样。2)用GYU对不同的GUTs进行了研究。发现汤川耦合存在等顶质量线，不能仅用顶质量M_t来区分同一线上的两个不同的GYU模型。如果它们在不同的行上，它们可以用M_t （IR）来区分。3)考虑将软超对称破缺扇区（SSB）纳入GYU程序，发现在具有GYU的软破缺超对称GUTs中存在一条具有通用性的SSB参数的RG不变和规则。此外，我们还发现这一普遍和规则在广泛的四维超弦模型中也被满足。根据这些结果，我们期望在GYU和超弦模型的超对称大统一之间存在密切的联系，我们希望沿着这条线的进一步研究可能会对基本粒子相互作用的理论本质有更深的理解。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