CKM矩阵的重整化群方程
Renormalization Group Equations for the CKM matrix
摘要：
本文用一种新的方法导出了标准模型的Cabibbo-Kobayashi-Maskawa矩阵的单圈重整化群方程及其双Higgs扩张和最小超对称扩张.导出的方程只依赖于夸克Yukawa耦合的重整化群方程的模型参数的子集，因此CKM矩阵演化不能完全检验夸克Yukawa耦合的重整化群演化.从导出的方程出发，我们得到了三种模型的重整化群演化的不变量，即幺正三角形的夹角$α$。对于标准模型的特殊情况和它的扩展与$v_{1}\approx v_{2}$，我们证明了，也是形状的么正三角形和Buras-Wolfenstein参数$\barρ=(1-{1/2}λ^{2})ρ$和$\barη=(1-{1/2}λ^{2})η$是保守的。幺正三角形的角的不变性意味着不可能找到一个模型，在这个模型中CKM矩阵在渐近能量下可能具有简单的特殊形式。
英文摘要：
We derive the one loop renormalization group equations for the Cabibbo-Kobayashi-Maskawa matrix for the Standard Model, its two Higgs extension and the minimal supersymmetric extension in a novel way. The derived equations depend only on a subset of the model parameters of the renormalization group equations for the quark Yukawa couplings so the CKM matrix evolution cannot fully test the renormalization group evolution of the quark Yukawa couplings. From the derived equations we obtain the invariant of the renormalization group evolution for three models which is the angle $α$ of the unitarity triangle. For the special case of the Standard Model and its extensions with $v_{1}\approx v_{2}$ we demonstrate that also the shape of the unitarity triangle and the Buras-Wolfenstein parameters $\barρ=(1-{1/2}λ^{2})ρ$ and $\barη=(1-{1/2}λ^{2})η$ are conserved. The invariance of the angles of the unitarity triangle means that it is not possible to find a model in which the CKM matrix might have a simple, special form at asymptotic energies.
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