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arXiv 0810.4813hep-phhep-th
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混合角的测量

Measures on Mixing Angles

Gary W. Gibbons, Steffen Gielen, C. N. Pope, Neil Turok

摘要:

我们解决了在标准模型中CP破坏的明显非常小的幅度的问题,用Jarlskog不变量J来度量。为了对J的某些值的概率做出陈述,我们试图在小林-Maskawa矩阵空间上找到一个自然的度量,即双商U(1)^2 \SU(3)/U(1)^2。我们回顾了几种可能的,几何动机的措施的选择,并计算这些措施的J的权力的期望值。我们发现,不同的选择措施一般使观察到的CP破坏的幅度出现微调。由于夸克质量和混合角是由同一组汤川耦合决定的,我们接着进行第二次计算,其中我们考虑了已知的夸克质量等级。我们在3 × 3厄米矩阵的空间上构造了一个最简单的测度,它再现了这个已知的层次结构。在第二种方法中计算J的幂的期望值,我们发现J的值现在很可能接近观察值,并且似乎没有任何微调。我们的研究结果表明,小林-Maskawa角的选择是密切相关的观察到的质量等级。最后,我们讨论中微子的相应情况。

英文摘要:

We address the problem of the apparently very small magnitude of CP violation in the standard model, measured by the Jarlskog invariant J. In order to make statements about probabilities for certain values of J, we seek to find a natural measure on the space of Kobayashi-Maskawa matrices, the double quotient U(1)^2\SU(3)/U(1)^2. We review several possible, geometrically motivated choices of the measure, and compute expectation values for powers of J for these measures. We find that different choices of the measure generically make the observed magnitude of CP violation appear finely tuned. Since the quark masses and the mixing angles are determined by the same set of Yukawa couplings, we then do a second calculation in which we take the known quark mass hierarchy into account. We construct the simplest measure on the space of 3 x 3 Hermitian matrices which reproduces this known hierarchy. Calculating expectation values for powers of J in this second approach, we find that values of J close to the observed value are now rather likely, and there does not seem to be any fine tuning. Our results suggest that the choice of Kobayashi-Maskawa angles is closely linked to the observed mass hierarchy. We close by discussing the corresponding case of neutrinos.

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