Dynamical Symmetry Breaking and Grand Unified Theoreis

本课题在1992 - 1993年两年的研究中取得了如下成果：1.在最小超对称标准模型中，利用重整化群方程研究了在SO（10）和E_6大统一理论所建议的边界条件下，是否可能解释顶夸克和底夸克之间的大质量比。我们证明了它可以通过QCD强相互作用和U（1）超荷和γ轻子引起的SU（2）R破坏的联合作用来实现。本文提出了一种新的求有效势的一般方法，使有效势满足重整化群方程。该方法结合解耦定理，可适用于任何具有多质量尺度的一般系统.指出Schwinger-Dyson方程和Bethe-Salpeter方程若满足外规范不变性，则必须相互相容。我们提出了一个系统的方法来满足这种规范不变性在任何阶近似.将改进的阶梯近似应用于重夸克介子的BS方程，计算了Isgur-Wise函数。我们的计算预测了几个百分比大CKM矩阵元素V_<cb>比其他计算。研究了一个包含强4-Fermi相互作用的单代费米子E_6大统一模型。我们发现，E_6对称性要么破缺为F_4，要么破缺为S_p（8），要么破缺为G_2，要么破缺为SU（3），这取决于两个4-费米相互作用的强度关系。

The research results of our project for two years in 1992 - 1993 are as follows :1. We studied in the minimal supersymmetric standard model by using renormalization group equation whether it is possible to explain the large mass ratio between top and bottom quarks under the boundary condition suggested by SO(10) and E_6 grand unified theories. We showed that it can be realized by a combined effect of QCD strong interaction and the SU(2)_R violation owing to U(1)-hypercharge and gamma-lepton.2. We presented a new general method for obtaining effective potential so as to satisfy the renormal-ization group equation. This method, combined with decoupling theorem, is made applicable to any general system possessing many mass scales.3. It is pointed out that the Schwinger-Dyson and Bethe-Salpeter equations have to have mutual con-sistencies if they satisfy external gauge invariance. We presented a systematic method for satisfying this gauge invariance at any order of approximation.4. Applying the improved ladder approximation for BS equation to heavy quark mesons, we calculated the Isgur-Wise function - a universal form factor. Our calculation predicts a few percent larger CKM matrix element V_<cb> than the other calculations.5. We studied an E_6 grand unified model of a single generation fermion which contains strong 4-fermi interactions. We found that the E_6 symmetry breaks down either to F_4 or to S_p(8) or G_2 or SU(3), depending on the strength relation of the two 4-fermi interactions.