Correlation of normal neutrino mass ordering with upper octant of $\theta^{}_{23}$ and third quadrant of $\delta$ via RGE-induced $\mu$-$\tau$ 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 $3\sigma$ level, and the best-fit values of the largest neutrino mixing angle $\theta^{}_{23}$ and the Dirac CP-violating phase $\delta$ are located in the higher octant and the third quadrant, respectively. We show that all these important issues can be naturally explained by the $\mu$-$\tau$ 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 $\tan\beta$ to vary in their reasonable regions.