arXiv 2012.122432020-12hep-phhep-th

小$θ_{13}$和来自$μ-τ$对称性的太阳中微子振荡参数

Small $θ_{13}$ and solar neutrino oscillation parameters from $μ-τ$ symmetry

Abdel Pérez-Lorenzana

备注：: Extended version. New discussions added. Six pages, one figure
DOI：: 10.1142/S0217751X21502250

摘要：

交换$μ-τ$对称性的有效马约拉纳中微子质量矩阵预测的最大混合大气中微子振荡除了零混合，不能直接确定与反应堆中微子振荡混合，$θ_{13}$，除非一个特定的顺序是假定的质量本征态。否则，已经在精确对称的水平上预测了$θ_{13}$的非零值。在这种情况下，太阳中微子的混合和尺度，以及正确的大气混合，都是由对称性破缺引起的。我提出了一个质量矩阵的建议，实现了这种情况下，$\tanθ_{13}$的小自然是由参数$ε\sim\sqrt{Δm^2_{sol}/Δm^2_{ATM}}$和太阳能混合的小$Δm^2_{sol}$。所提出的矩阵保持稳定的重整化效应下，它也允许占CP破坏在预期的区域内没有进一步的约束。

英文摘要：

Exchange $μ-τ$ symmetry in the effective Majorana neutrino mass matrix does predict a maximal mixing for atmospheric neutrino oscillations asides to a null mixing that cannot be straightforwardly identified with reactor neutrino oscillation mixing, $θ_{13}$, unless a specific ordering is assumed for the mass eigenstates. Otherwise, a non zero value for $θ_{13}$ is predicted already at the level of an exact symmetry. In this case, solar neutrino mixing and scale, as well as the correct atmospheric mixing, arise from the breaking of the symmetry. I present a mass matrix proposal for normal hierarchy that realizes this scenario, where the smallness of $\tanθ_{13}$ is naturally given by the parameter $ε\sim\sqrt{Δm^2_{sol}/Δm^2_{ATM}}$ and the solar mixing is linked to the smallness of $Δm^2_{sol}$. The proposed matrix remains stable under renormalization effects and it also allows to account for CP violation within the expected region without further constrains.

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