Dynamical Symmetry Breaking and Grand Unified Theoreis

动力学对称破缺与大统一理论

基本信息

批准号：
04640292
负责人：
KUGO Taichi
金额：
$ 1.34万
依托单位：
KYOTO UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1992
资助国家：
日本
起止时间：
1992 至 1993
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-04640292/
关键词：
Grand Unified Theory Effective Potential Schwinger-Dyson equation Bethe-Salpeter equation Renormalization Group equation Decoupling theorem Isgur-Wise function ゲージ不変性 Improved Ladder近似 E_6対称性 heavy quark horizontal symmetry Schwing

项目摘要

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.

本项目1992-1993两年间的研究成果如下： 1．我们在最小超对称标准模型中，利用重正化群方程研究了SO(10)和E_6大统一理论所提出的边界条件下是否可以解释顶夸克和底夸克之间的大质量比。我们证明它可以通过QCD强相互作用和U(1)-超电荷和γ-轻子引起的SU(2)_R违规的综合作用来实现。2．我们提出了一种新的通用方法来获得有效势以满足重正化群方程。该方法与解耦定理相结合，适用于任何具有多个质量尺度的通用系统。 3．指出Schwinger-Dyson 方程和Bethe-Salpeter 方程若满足外规范不变性，则必须具有相互一致性。我们提出了一种系统方法来满足任意近似阶的规范不变性。4．将 BS 方程的改进阶梯近似应用于重夸克介子，我们计算了 Isgur-Wise 函数 - 一个通用形状因子。我们的计算预测 CKM 矩阵元素 V_<cb> 比其他计算大几个百分点。5。我们研究了单代费米子的 E_6 大统一模型，其中包含强 4-费米相互作用。我们发现 E_6 对称性会分解为 F_4 或 S_p(8) 或 G_2 或 SU(3)，具体取决于两个 4-费米相互作用的强度关系。