论文标题
$ ldl^{t} $分解的公式，用于最小的I类型机制和$ CP $对称的条件在任意的基础上
A formula by $LDL^{T}$ decomposition for the minimal type-I seesaw mechanism and conditions of $CP$ symmetry in an arbitrary basis
论文作者
论文摘要
在本文中，通过$ ldl^{t} $分解为最小的I Seesaw机制定义一个公式，我们在任意的基础上获得了中微子质量矩阵$ m $的$ CP $对称条件。发现条件为$ {\ rm re \，}（m_ {22} a_ {i} - m_ {12} b_ {i}）\，{\ rm im \，}（m_ {22} a_ {j} a_ {j} a { b_ {i} \，{\ rm im \，} b_ {j} $或$ = - \ det m \，{\ rm im \，} b_ {i} \，{\ rm re \ \ \ rm re \，} b_ {j} $ b_ {j}）$和右撇子中微子质量矩阵$ m_ {ij} $。换句话说，$ b_ {i} $的真实或虚构部分必须与数量$（m_ {22} a_ {i} -m_ {12} b_ {i}）$成比例。
In this paper, defining a formula by $LDL^{T}$ decomposition for the minimal type-I seesaw mechanism, we obtain conditions of $CP$ symmetry for the neutrino mass matrix $m$ in an arbitrary basis. The conditions are found to be ${\rm Re\,} (M_{22} a_{i} - M_{12} b_{i}) \, {\rm Im \,} ( M_{22} a_{j} - M_{12} b_{j}) = - \det M \, {\rm Re\,} b_{i} \, {\rm Im \,} b_{j}$ or $ = - \det M \, {\rm Im \,} b_{i} \, {\rm Re\,} b_{j}$ for the Yukawa matrix $Y_{ij} = (a_{j}, b_{j})$ and the right-handed neutrino mass matrix $M_{ij}$. In other words, the real or imaginary part of $b_{i}$ must be proportional to the real or imaginary part of the quantity $(M_{22} a_{i} - M_{12} b_{i})$.
