arXiv 1012.60282010-12hep-ph

味对称与大统一

Flavor Symmetry and Grand Unification

Berthold Stech

备注：: 6 pages, improvements of c- coefficients and presentation, no change of the light Higgs mass value

摘要：

味对称与大统一的组合被认为是：大统一$ \times$味。为了容纳三代，使用了味道群SO（3）。所有的费米子都在这个群下变换为3-矢量。Yukawa耦合由Flavon场的真空期望值得到。对于flavon场（相对于大统一理论群的单线态）和希格斯场（相对于生成群的单线态），假设了一种简单的有效势形式。它自动导致这些标量场的自发对称性破缺。离散的S ~ 4变换将势的极小值的不同位置联系起来，这些势可以用来描述著名的上夸克质量谱的层次结构。在大统一模型中希格斯场质量的巨大等级也可以用这种方式参数化。它导致了最轻的希格斯玻色子的质量的预测，根据其真空期望值$v_0$：$ m_{Higgs} = \frac{v_0}{\sqrt{2}} = 123 GeV$。

英文摘要：

The combination of flavor symmetries with grand unification is considered: GUT $ \times$ flavor . To accommodate three generations the flavor group SO(3) is used. All fermions transform as 3-vectors under this group. The Yukawa couplings are obtained from vacuum expectation values of flavon fields. For the flavon fields (singlets with respect to the GUT group) and the Higgs fields (singlets with respect to the generation group) a simple form for the effective potentials is postulated. It automatically leads to spontaneous symmetry breaking for these scalar fields. Discrete S4 transformations relate the different locations of the minima of the potentials.These potentials can be used to describe the hierarchy of the well known up quark mass spectrum. Also the huge hierarchy of the masses of the Higgs fields in grand unified models can be parametrized in this way. It leads to a prediction of the mass of the lightest Higgs boson in terms of its vacuum expectation value $v_0$: $ m_{Higgs} = \frac{v_0}{\sqrt{2}} = 123 GeV$.

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