Dynamical Symmetry Breaking and Grand Unified Theoreis

1.在极小超对称标准模型中，我们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，能否解释顶、底夸克的大质量比。结果表明，它可以由QCD强相互作用和U(1)超荷和伽马轻子引起的SU(2)_R破坏共同作用来实现。为了满足重整化群方程，我们提出了一种新的求有效势的一般方法。该方法与解耦定理相结合，适用于任何具有多质量尺度的一般系统。指出如果Schwinger-Dyson方程和Bethe-Salpeter方程满足外规范不变性，则它们必须相互协调。我们给出了一种系统的方法来满足任意阶近似下的规范不变性。将改进的BS方程梯形近似应用于重夸克介子，计算了一个普遍的形状因子--Isgur-Wise函数。我们的计算预测CKM矩阵元素V_&lt；CB&gt；比其他计算大几个百分点。我们研究了包含强4-费米相互作用的单代费米子的E_6大统一模型。我们发现，根据两个4-费米相互作用的强度关系，E_6对称性可以分解为F_4或S_p(8)或G_2或SU(3)。

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.