Weinberg算子三环实现的系统分类
Systematic classification of three-loop realizations of the Weinberg operator
摘要：
本文系统地研究了Weinberg算子的三环阶分解。有超过四千个连接的拓扑。然而，这些绝大多数是无限的修正低阶中微子质量图，只有一个非常小的百分比产量模型的三环图是领先的订单贡献的中微子质量矩阵。我们确定了73个拓扑结构，可以导致真正的三圈模型与费米子和标量，即模型的低阶图自动缺席，而不需要调用额外的对称性。73个真拓扑又可分为两个子类：正常真拓扑（44例）和特殊真拓扑（29例）。后者是一类特殊的拓扑结构，只有在非常具体的领域选择中才能得到真正的图。真正的拓扑结构产生374个图在弱基，这可以减少到只有30个不同的图在质量本征态基础。我们还讨论了如何所有的质量本征态图可以描述只有五个主积分。我们提出了一些具体的模型，其中两个，我们给出了它们产生的中微子质量的典型大小的数值估计。我们的结果可以很容易地应用于构造其他具有三圈结构的$d=5$中微子质量模型。
英文摘要：
We study systematically the decomposition of the Weinberg operator at three-loop order. There are more than four thousand connected topologies. However, the vast majority of these are infinite corrections to lower order neutrino mass diagrams and only a very small percentage yields models for which the three-loop diagrams are the leading order contribution to the neutrino mass matrix. We identify 73 topologies that can lead to genuine three-loop models with fermions and scalars, i.e. models for which lower order diagrams are automatically absent without the need to invoke additional symmetries. The 73 genuine topologies can be divided into two sub-classes: Normal genuine ones (44 cases) and special genuine topologies (29 cases). The latter are a special class of topologies, which can lead to genuine diagrams only for very specific choices of fields. The genuine topologies generate 374 diagrams in the weak basis, which can be reduced to only 30 distinct diagrams in the mass eigenstate basis. We also discuss how all the mass eigenstate diagrams can be described in terms of only five master integrals. We present some concrete models and for two of them we give numerical estimates for the typical size of neutrino masses they generate. Our results can be readily applied to construct other $d=5$ neutrino mass models with three loops.
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