Correlation of normal neutrino mass ordering with upper octant of $θ^{}_{23}$ and third quadrant of $δ$ via RGE-induced $μ$-$τ$ symmetry breaking

Abstract

The recent global analysis of three-flavor neutrino oscillation data indicates that the {\it normal} neutrino mass ordering is favored over the inverted one at the $3σ$ level, and the best-fit values of the largest neutrino mixing angle $θ^{}_{23}$ and the Dirac CP-violating phase $δ$ are located in the higher octant and the third quadrant, respectively. We show that all these important issues can be naturally explained by the $μ$-$τ$ reflection symmetry breaking of massive neutrinos from a superhigh energy scale down to the electroweak scale due to the one-loop renormalization-group equations (RGEs) in the minimal supersymmetric standard model (MSSM). The complete parameter space is explored {\it for the first time} in both Majorana and Dirac cases, by allowing the smallest neutrino mass $m^{}_1$ and the MSSM parameter $\tanβ$ to vary in their reasonable regions.