arXiv 1306.18902013-06hep-ph

轻子与无质量中微子的水平对称性

Horizontal symmetries of leptons with a massless neutrino

Anjan S. Joshipura, Ketan M. Patel

备注：: 18 pages; a new section added, conclusions unchanged, version accepted for publication in Physics Letters B
发表信息：: Phys.Lett. B727 (2013) 480-487
DOI：: 10.1016/j.physletb.2013.11.003

摘要：

讨论了中微子质量矩阵与无质量中微子的剩余对称性$G_ν$以及$G_ν$和带电轻子质量矩阵的剩余对称性$G_l$在有限离散群$G$中的嵌入.如果$G_ν$和$G$是$U(3)$的子群，而不是$SU(3)$的子群，则会产生无质量中微子。在三个具体的例子中讨论了所得到的轻子混合矩阵$U_{PMNS}$的结构，这些例子基于（a）$Σ(3N^3)$、（b）$Σ(2N^2)$和（c）$S_4(2) \equiv A_4\rtimes Z_4$。$Σ(3N^3)$组能够正确再现$U_{PMNS}$的第二列或第三列。如果中微子质量等级被颠倒，$Σ(2N^2)$群分别导致反应堆和大气混合角的预测$θ_{13}=0$，$θ_{23}=\fracπ{4}$。在这种情况下，太阳角仍然是不确定的。当$G=S_4(2)$可以为反向层次结构提供双极大混合时，也可以确定这一点。示例（b）和（c）提供了对与无质量中微子的现实轻子混合的良好零阶近似。我们还给出了一个基于$S_4(2)$对称性的具体模型的例子，得到了一个无质量的中微子和可行的轻子混合角。

英文摘要：

Residual symmetry $G_ν$ of neutrino mass matrix with a massless neutrino and embedding of $G_ν$ and the residual symmetry $G_l$ of the charged lepton mass matrix into finite discrete groups $G$ is discussed. Massless neutrino results if $G_ν$ and hence $G$ are subgroups of $U(3)$ rather than of $SU(3)$. Structure of the resulting leptonic mixing matrix $U_{PMNS}$ is discussed in three specific examples based on groups (a) $Σ(3N^3)$, (b) $Σ(2N^2)$ and (c) $S_4(2) \equiv A_4\rtimes Z_4$. $Σ(3N^3)$ groups are able to reproduce either the second or the third column of $U_{PMNS}$ correctly. $Σ(2N^2)$ groups lead to prediction $θ_{13}=0$, $θ_{23}=\fracπ{4}$ for the reactor and atmospheric mixing angles respectively if neutrino mass hierarchy is inverted. Solar angle remains undetermined in this case. This also gets determined when $G=S_4(2)$ which can give bi-maximal mixing for inverted hierarchy. Examples (b) and (c) provide a good zeroth order approximation to realistic leptonic mixing with a massless neutrino. We also present an example of the specific model based on $S_4(2)$ symmetry in which a massless neutrino and viable leptonic mixing angles are obtained.

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