Radiative corrections and explicit perturbations to the tetra-maximal neutrino mixing with large θ13

Abstract

The tetra-maximal neutrino mixing pattern predicts a relatively large reactor mixing angle θ 13 ≈ 8.4 • , which is in good agreement with the latest best-fit value θ 13 = 9 • . However, its prediction for θ 12 ≈ 30.4 • is inconsistent with current oscillation data at the 3σ C.L. We show that explicit perturbations to the tetra-maximal mixing can naturally enhance θ 12 to its best-fit value θ 12 = 34 • .Furthermore, we demonstrate that if the tetra-maximal mixing is produced by a certain flavor symmetry at a high-energy scale Λ = 10 14 GeV, significant radiative corrections in the minimal supersymmetric standard model can modify θ 12 to be compatible with experimental data at the electroweak scale Λ EW = 10 2 GeV. The predictions for θ 13 ≈ 8.4 • and θ 23 = 45 • , as well as the CP-violating phases ρ = σ = −δ = 90 • , are rather stable against radiative corrections.

Resolving the octant ofθ23via radiativeμ−τsymmetry breaking

“…In this connection a few constant neutrino mixing patterns which possess |U µi | = |U τ i |, such as the bimaximal [20] and tri-bimaximal [21] ones with θ 13 = 0 • and θ 23 = 45 • , have been assumed at a superhigh energy scale; and their RGE running behaviors have been investigated mainly to see whether a finite θ 13 can be radiatively generated at low energies [18]. The closest example of this kind should be the work [22] on radiative corrections to the tetra-maximal neutrino mixing pattern [23], in which θ 13 ≃ 8.4 • , θ 23 = 45 • and δ = 90 • or 270 • have been predicted. Our present work is different from the previous ones in several aspects: (a) it is not subject to any explicit neutrino mixing pattern; (b) it focuses on the PMNS µ-τ asymmetries ∆ i and its RGE evolution; (c) it provides a reasonable resolution to the octant of θ 23 by attributing it to the PMNS µ-τ symmetry breaking effect; (d) it may also resolve the quadrant of δ in a similar way.…”

The µ–τ reflection symmetry of Majorana neutrinos *

“…2)] ≃ 8.4 • besides equation (1.18). We find that U 4M can fit current neutrino oscillation data after slight µ-τ reflection symmetry breaking effects are taken into account [62,63]. A number of interesting constant neutrino mixing patterns respecting the µ-τ permutation symmetry have also been proposed and discussed in the literature [10].…”

Breaking of the tetra-maximal neutrino mixing pattern

“…[14], in presence of latest oscillation data [2,9,10] 2 . The breaking effect of such symmetry has been examined in [15]. The tetra-maximal mixing matrix can be decomposed into four maximal rotations…”