Abstract
The latest global analysis of neutrino oscillation data indicates that the normal neutrino mass ordering is favored over the inverted one at the 3 σ level. 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 these experimental trends can be naturally explained by the μ - τ reflection symmetry breaking, triggered by the one-loop renormalization-group equations (RGEs) running from a superhigh energy scale down to the electroweak scale in the framework of the minimal supersymmetric standard model (MSSM). The complete parameter space is numerically explored for both the Majorana and Dirac cases, by allowing the smallest neutrino mass m 1 and the MSSM parameter tan β to vary within their reasonable ranges.
Highlights
In the last twenty years, we have witnessed compelling evidence of the neutrino oscillation phenomena [1], as recognized by both the 2015 Nobel Prize in Physics and the 2016 Breakthrough Prize in Fundamental Physics
We show that the normal neutrino mass ordering, the upper-octant of θ23, and the third-quadrant of δ can be naturally correlated via the renormalization-group equations (RGEs)-induced μ-τ reflection symmetry-breaking effect in the minimal supersymmetric standard model (MSSM) framework
The latest global analysis suggests this symmetry should be broken at the low energy experimental scale
Summary
In the last twenty years, we have witnessed compelling evidence of the neutrino oscillation phenomena [1], as recognized by both the 2015 Nobel Prize in Physics and the 2016 Breakthrough Prize in Fundamental Physics. It is popular to introduce some heavy degrees of freedom (i.e., the seesaw mechanism [4,5,6,7,8]) and certain flavor symmetries at a superhigh energy scale to explain the smallness of neutrino masses and the lepton flavor mixing patterns observed at low energies In this case, we need to run the renormalization-group equations (RGEs) to bridge the gap between these two scales. The μ-τ reflection symmetry [12,13,14], the minimal discrete flavor symmetry responsible for the nearly maximal atmospheric neutrino mixing and potentially maximal CP violation in neutrino oscillations, can naturally lead to θ23 = 45◦ and δ = 270◦ Assuming this symmetry is realized at a superhigh energy scale, such as the seesaw scale Λμτ , it can be spontaneously broken at the electroweak scale ΛEW ∼102 GeV because of the RGE running effect, leading to the deviations of (θ23 , δ) from (45◦ , 270◦ ). Our in-depth analysis is timely, general, and suggestive
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