Correlation of normal neutrino mass ordering with upper octant of θ23 and third quadrant of δ via RGE-induced μ-τ symmetry breaking** Supported by the National Natural Science Foundation of China (11775231, 11775232)

Guo-Yuan Huang,Zhi-Zhong Xing,Jing-Yu Zhu

doi:10.1088/1674-1137/42/12/123108

Abstract

The recent global analysis of three-flavor neutrino oscillation data indicates that the 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 θ23 and the Dirac CP-violating phase δ are located in the higher octant and 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 owing to the one-loop renormalization-group equations (RGEs) in the minimal supersymmetric standard model (MSSM). The complete parameter space is explored for the first time in both the Majorana and Dirac cases, by allowing the smallest neutrino mass m1 and the MSSM parameter tanβ to vary within their reasonable regions.

Highlights

The striking phenomena of solar, atmospheric, reactor and accelerator neutrino oscillations have all been observed in the past twenty years [1], demonstrating that the standard model (SM) of particle physics is by no means complete and must be extended to explain both the origin of finite but tiny neutrino masses and the origin of large lepton flavor mixing effects
The smallness of neutrino masses might be attributed to the existence of some heavy degrees of freedom at a superhigh energy scale — a popular idea known as the seesaw mechanism [2]; and the largeness of neutrino mixing angles and CP-violating phases might originate from an underlying flavor symmetry [3, 4], which should manifest itself at a superhigh energy scale
A global analysis of currently available data on neutrino oscillations indicates that the normal neutrino mass ordering (m1 < m2 < m3) is favored over the inverted one (m3 < m1 < m2) at the 3σ level 1 the best-fit value of the largest neutrino mixing angle θ23 is slightly larger than 45◦, and the best-fit value of the Dirac phase δ is somewhat smaller than 270◦ [8,9]

Summary

Introduction

The striking phenomena of solar, atmospheric, reactor and accelerator neutrino oscillations have all been observed in the past twenty years [1], demonstrating that the standard model (SM) of particle physics is by no means complete and must be extended to explain both the origin of finite but tiny neutrino masses and the origin of large lepton flavor mixing effects. In this paper we show that the normal neutrino mass ordering, the slightly higher octant of θ23 and the possible location of δ in the third quadrant can be naturally correlated and explained via RGE-induced μ-τ reflection symmetry breaking of massive neutrinos — namely, via the one-loop RGE evolution of neutrino masses and flavor mixing parameters from Λμτ ∼ 1014 GeV down to ΛEW ∼ 102 GeV in the minimal supersymmetric standard model (MSSM). This kind of correlation will soon be tested by more accurate experimental data.

The Majorana case

The Dirac case

Numerical exploration of the parameter space

Concluding remarks