The $\mu -\tau$ reflection symmetry of Dirac neutrinos and its breaking effect via quantum corrections

Abstract

Given the Dirac neutrino mass term, we explore the constraint conditions which allow the corresponding mass matrix to be invariant under the μ-τreflection transformation, leading us to the phenomenologically favored predictions θ_{23} = π/4 and δ= 3π/2 in the standard parametrization of the 3\times 3 lepton flavor mixing matrix. If such a flavor symmetry is realized at a superhigh energy scale Λ_{μτ}, we investigate how it is spontaneously broken via the one-loop renormalization-group equations (RGEs) running from Λ_{μτ} down to the Fermi scale Λ_{\rm F}. Such quantum corrections to the neutrino masses and flavor mixing parameters are derived, and an analytical link is established between the Jarlskog invariants of CP violation at Λ_{μτ} and Λ_{\rm F}. Some numerical examples are also presented in both the minimal supersymmetric standard model and the type-II two-Higgs-doublet model, to illustrate how the octant of θ_{23}, the quadrant of δand the neutrino mass ordering are correlated with one another as a result of the RGE-induced μ-τreflection symmetry breaking effects.

arXiv comment21 pages, 4 figures, some changes made, 2HDM considered, accepted for publication in JHEP

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