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首页> 外文期刊>Physical review, D >Fully constrained mass matrix: Can symmetries alone determine the flavon vacuum alignments?
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Fully constrained mass matrix: Can symmetries alone determine the flavon vacuum alignments?

机译：完全约束的质量矩阵：可以单独对称测定黄金真空对齐吗？

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In the framework of the representation theory of finite groups, it was recently shown that a fully constrained complex-symmetric mass matrix can be conveniently mapped into a sextet of Σ ( 72 × 3 ) . In this paper, we introduce an additional flavor group X 24 in the model so that the vacuum alignment of the Σ ( 72 × 3 ) sextet is determined not only by the symmetries of Σ ( 72 × 3 ) but also by that of X 24 . We define several flavons which transform as multiplets under Σ ( 72 × 3 ) as well as X 24 . The vacuum alignment of each of these flavons is obtained as a simultaneous invariant eigenstate of specific elements of the groups Σ ( 72 × 3 ) and X 24 ; i.e., the vacuum alignment is fully determined by its residual symmetries. These flavons couple together uniquely resulting in the fully constrained sextet of Σ ( 72 × 3 ) . Through this work we propose a general formalism in which the flavor symmetry group ( G f ) is obtained as the direct product, G f = G r × G x . Fermions transform nontrivially only under G r while they remain invariant under G x . Flavons, on the other hand, transform nontrivially under both G r and G x . The vacuum alignment of each flavon multiplet transforming irreducibly under G r × G x is uniquely identified by its corresponding residual symmetry (a subgroup of G r × G x ). Several such flavons couple together to form an effective multiple of G r which remains invariant under G x . This effective multiplet couples to the fermions.
机译：在有限组的表示理论的框架中，最近近来可以将完全约束的复杂对称质量矩阵方便地映射到σ（72×3）的六分。在本文中，我们在模型中引入额外的风味组X 24，使得σ（72×3）施×的真空对准不仅由σ（72×3）的对称而不是x 24的对称来确定。我们定义了几种形式的Flavons，它在σ（72×3）下的多重以及X 24中变换。将这些黄菌菌素的真空对准作为组σ（72×3）和x 24的特定元素的同时不变的特征酯。即，真空对准完全由其残余对称确定。这些FlavOns耦合在一起，导致完全约束的σ（72×3）。通过这项工作，我们提出了一种一般形式主义，其中获得了风味对称组（G F）作为直接产品，G F = G r×g x。污物仅在G x下不变时不变地变换在g r下。另一方面，味道，在G r和g x两者下，不动化。通过其相应的残余对称（G R×G X的子组）唯一地识别每个FLAVON乘法变换的每个FLAVON多功能率变换的真空对准。若干这样的氟锭将耦合在一起形成一个有效的g r，它仍然不变于g x。这种有效的多重耦合到费米。

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