论文标题
中微子混合的几何相
Geometric phases in neutrino mixing
论文作者
论文摘要
由于质量和风味本征态之间的非平凡混合，中微子可以获得动态和几何阶段。在本文中，我们使用运动学方法中三种风味中微子模型中所有合理规格不变的对角线和偏离几何阶段的一般表达式。我们发现，对角线和高阶偏高几何阶段对质量顺序和违反阶段$δ$的dirac CP敏感。我们表明，在任何环状或非环状置于风味指数的循环置换率零时，三阶几何几何相（$φ_{μeeτ} $）都是不变的。对于非零$δ$，我们发现$φ_{μeτ}（δ）=φ________________________________________________。此外，我们使用两个风味中微子模型探索了物质背景的效果，并表明对角几何阶段在MSW共振区域中为0或$π$，并且在其他地方将非平凡的值。零与$π$之间的过渡发生在称为节点点的完整振荡反转点，其中未定义对角线几何相。同样，在两个风味的近似值中，相对于混合角度，两个不同的对角线几何阶段是共同函数。最后，在两个风味模型中，我们表明唯一的二阶偏外几何阶段是拓扑数量的数量，并且始终是$π$。
Neutrinos can acquire both dynamic and geometric phases due to the non-trivial mixing between mass and flavour eigenstates. In this article, we derive the general expressions for all plausible gauge invariant diagonal and off-diagonal geometric phases in the three flavour neutrino model using the kinematic approach. We find that diagonal and higher order off-diagonal geometric phases are sensitive to the mass ordering and the Dirac CP violating phase $δ$. We show that, third order off-diagonal geometric phase ($Φ_{μeτ}$) is invariant under any cyclic or non-cyclic permutations of flavour indices when the Dirac CP phase is zero. For non-zero $δ$, we find that $Φ_{μeτ}(δ)=Φ_{e μτ}(-δ)$. Further, we explore the effects of matter background using a two flavour neutrino model and show that the diagonal geometric phase is either 0 or $π$ in the MSW resonance region and takes non-trivial values elsewhere. The transition between zero and $π$ occurs at the point of complete oscillation inversion called the nodal point, where the diagonal geometric phase is not defined. Also, in two flavour approximations, two distinct diagonal geometric phases are co-functions with respect to the mixing angle. Finally, in the two flavour model, we show that the only second order off-diagonal geometric phase is a topological invariant quantity and is always $π$.
