Resolving the octant of theta_{23} via radiative mu-tau symmetry breaking

TL;DR

This paper proposes that the observed neutrino mixing pattern, especially the deviation of theta_{23} from 45°, can be explained by small mu-tau symmetry breaking via renormalization-group equations, linking high-energy symmetry to low-energy measurements.

Contribution

It demonstrates that the mu-tau symmetry at high energy scales naturally leads to the observed neutrino mixing angles through RGE effects, with a specific correlation to neutrino mass ordering.

Findings

RGE corrections can account for the deviation of theta_{23} from 45° at low energies.

The value of theta_{23} at low energy is correlated with neutrino mass ordering.

Delta can evolve from 270° at high energy regardless of neutrino nature (Dirac or Majorana).

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.