Title: Neutrino Mass Matrix Predicted From Symmetric Texture Show Chinese title

Title: 从对称纹理预测中微子质量矩阵

Abstract: Within the framework of grand unified theories, we make full analysis of symmetric texture to see if such texture can reproduce large neutrino mixings, which have recently been confirmed by the observed solar and atmospheric neutrino oscillation experiments. It is found that so-called symmetric texture with anomalous U(1) family symmetry with Froggatt-Nielsen mechanism does not provide a natural explanation of two large mixing angles. On the contrary we should adopt "zero texture" which have been extensively studied by many authors and only this scenario can reproduce two large mixing angles naturally. Under such "zero texture" with minimal symmetric Majorana matrix, all the neutrino masses and mixing angles, 6 quantities, are expressed in terms of up-quark masses, $m_t,m_c,m_u$ with two adjustable parameters. This provides interesting relations among neutrio mixing angles, $\tan^2 2\theta_{12} \simeq \frac{144m_c}{m_t} \tan^2 2\theta_{23} \cos^2 \theta_{23}, \quad \sin^2 \theta_{13} \simeq \frac{4m_c}{m_t}\sin^2 \theta_{23} \cos^2 \theta_{12}$. Thus $|U_{e3}|$ is predicted to lie within the range $0.01-0.06$. Also absolute masses of three neutrinos are predicted almost uniquely. This is quite in contrast to the case where bi-large mixings come from the charged lepton sector with non-symmetric mass matrix, which does not provide the information of neutrino masses. Show Chinese abstract

Abstract: 在大统一理论的框架下，我们对对称纹理进行了全面分析，以查看这种纹理是否可以再现最近通过观测太阳和大气中微子振荡实验确认的大中微子混合。 发现所谓的具有异常U(1)家族对称性的对称纹理以及Froggatt-Nielsen机制并不能自然地解释两个大的混合角。 相反，我们应该采用“零纹理”，这已经被许多作者广泛研究，只有这种情形才能自然地再现两个大的混合角。 在这种“零纹理”和最小对称马约拉纳矩阵下，所有中微子质量与混合角，共6个量，都可以用上夸克质量来表示，$m_t,m_c,m_u$有两个可调参数。 这提供了中微子混合角之间的有趣关系，$\tan^2 2\theta_{12} \simeq \frac{144m_c}{m_t} \tan^2 2\theta_{23} \cos^2 \theta_{23}, \quad \sin^2 \theta_{13} \simeq \frac{4m_c}{m_t}\sin^2 \theta_{23} \cos^2 \theta_{12}$。 因此，$|U_{e3}|$被预测位于范围$0.01-0.06$内。 同时三种中微子的绝对质量也被预测几乎唯一。 这与来自带电轻子区的非对称质量矩阵的双大混合情况形成鲜明对比，后者无法提供中微子质量的信息。