通过离散味对称将Trinity推广到标量扇区
Extending Trinity to the Scalar Sector through Discrete Flavoured Symmetries
摘要：
我们推测基本标量和费米子之间的关系的存在，使得它似乎有可能存在三个希格斯二重态。我们引入了一个三位一体原则（TP），鉴于没有无质量夸克的事实，需要存在至少三个希格斯双重态。TP指出，一个给定电荷的夸克的质量矩阵的每一条线都应该得到一个且只有一个标量二重态的贡献，而且一个给定的标量二重态应该贡献给一个给定电荷的夸克的质量矩阵的一条且只有一条线。该原理类似于Anhow和Weinberg的天然风味保持（NFC），其关键区别在于NFC需要引入风味盲对称性，而TP需要以自然方式实现风味对称性。我们提供了两个例子，满足三位一体原则的基础上$\mathbb{Z}_3$和$\mathbb{Z}_2\times\mathbb{Z}_2'$味对称性，并表明它们是最小的多希格斯扩展的标准模型CP可以施加作为一个对称性的完整的拉格朗日和打破的真空，而不需要软破缺条款。我们表明，真空阶段是足以产生一个复杂的CKM矩阵，与实验一致。上述风味对称性导致汤川相互作用中参数数量的大幅减少，从而能够控制标量风味变化中性耦合（SFCNC）。我们分析了这两个模型的其他一些物理意义，包括对CP破坏的新来源所提供的宇宙重子不对称性的增强的估计，以及对它们的树级SFCNC的强度的讨论。
英文摘要：
We conjecture the existence of a relation between elementary scalars and fermions, making it plausible the existence of three Higgs doublets. We introduce a Trinity Principle (TP) which, given the fact that there are no massless quarks, requires the existence of a minimum of three Higgs doublets. The TP states that each line of the mass matrix of a quark of a given charge should receive the contribution from one and only one scalar doublet and furthermore a given scalar doublet should contribute to one and only one line of the mass matrix of a quark of a given charge. This principle is analogous to the Natural Flavour Conservation (NFC) of Glashow and Weinberg with the key distinction that NFC required the introduction of a flavour blind symmetry, while the TP requires a flavoured symmetry, to be implemented in a natural way. We provide two examples which satisfy the Trinity Principle based on $\mathbb{Z}_3$ and $\mathbb{Z}_2\times\mathbb{Z}_2'$ flavoured symmetries, and show that they are the minimal multi-Higgs extensions of the Standard Model where CP can be imposed as a symmetry of the full Lagrangian and broken by the vacuum, without requiring soft-breaking terms. We show that the vacuum phases are sufficient to generate a complex CKM matrix, in agreement with experiment. The above mentioned flavoured symmetries lead to a strong reduction in the number of parameters in the Yukawa interactions, enabling a control of the Scalar Flavour Changing Neutral Couplings (SFCNC). We analyse some of the other physical implications of the two models, including an estimate of the enhancement of the Baryon Asymmetry of the Universe provided by the new sources of CP violation, and a discussion of the the strength of their tree-level SFCNC.
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