Resolving the octant ofθ23via radiativeμ−τsymmetry breaking

Abstract

We point out that the observed neutrino mixing pattern at low energies is very likely to originate from the 3 times 3 lepton flavor mixing matrix U which possesses the exact mu-tau permutation symmetry |U_{mu i}| = |U_{tau i}| (for i=1,2,3) at a superhigh energy scale Lambda_{mu tau} \sim 10^{14} GeV. The deviation of theta_{23} from 45^\circ and that of delta from 270^\circ in the standard parametrization of U are therefore a natural consequence of small mu-tau symmetry breaking via the renormalization-group equations (RGEs) running from Lambda_{mu tau} down to the electroweak scale Lambda_{EW} \sim 10^2 GeV. In fitting current experimental data we find that the RGE-corrected value of theta_{23} is uniquely correlated with the neutrino mass ordering: theta_{23} \simeq 42.4^\circ reported by Capozzi et al (or theta_{23} \simeq 48.9^\circ reported by Forero et al) at Lambda_{EW} can arise from theta_{23} = 45^\circ at Lambda_{mu tau} in the minimal supersymmetric standard model if the neutrino mass ordering is inverted (or normal). Accordingly, the preliminary best-fit results of delta at Lambda_{EW} can also evolve from delta = 270^\circ at Lambda_{mu tau} no matter whether the massive neutrinos are Dirac or Majorana particles.