论文标题
重新归一化组方程的连续和离散对称性中微子振荡的物质振荡
Continuous and Discrete Symmetries of Renormalization Group Equations for Neutrino Oscillations in Matter
论文作者
论文摘要
可以用三个有效的中微子质量$ \ widetilde {m}^{} _ i $（对于$ i = 1、2、3 $）和有效混合矩阵$ v^{} _ {αi} $（$ i = 1、2、3 $）（对于$ i = 1、2、3 $）来描述物质的三效中微子振荡。当物质参数$ a \ equiv 2 \ sqrt {2} g^{} _ {\ rm f} n^{} n^{} _ e e $被视为一个自变量，一组完整的一阶普通微分方程，用于$ \ wideTilde {m} m}^2_i $ and $ | v^^{} {} {} {} {} {} {^a}作品。在本文中，我们指出，这种微分方程系统既具有以单参数谎言基团为特征的连续对称性，又具有与三个中微子质量特征状态的排列相关的离散对称性。讨论了这些对称性对解决微分方程和寻找差异不变的含义。
Three-flavor neutrino oscillations in matter can be described by three effective neutrino masses $\widetilde{m}^{}_i$ (for $i = 1, 2, 3$) and the effective mixing matrix $V^{}_{αi}$ (for $α= e, μ, τ$ and $i = 1, 2, 3$). When the matter parameter $a \equiv 2\sqrt{2} G^{}_{\rm F} N^{}_e E$ is taken as an independent variable, a complete set of first-order ordinary differential equations for $\widetilde{m}^2_i$ and $|V^{}_{αi}|^2$ have been derived in the previous works. In the present paper, we point out that such a system of differential equations possesses both the continuous symmetries characterized by one-parameter Lie groups and the discrete symmetry associated with the permutations of three neutrino mass eigenstates. The implications of these symmetries for solving the differential equations and looking for differential invariants are discussed.
