Diagonal reflection symmetries, four-zero texture, and trimaximal mixing with predicted θ13 in an A4 symmetric model

Abstract

Abstract In this paper, we impose a magic symmetry on the neutrino mass matrix mν with universal four-zero texture and diagonal reflection symmetries. Due to the magic symmetry, the Maki–Nakagawa–Sakata matrix inevitably has trimaximal mixing. Since the lepton sector has only six free parameters, the physical observables of leptons are all determined from the charged lepton masses mei, the neutrino mass differences $\Delta m_{i1}^{2}$, and the mixing angle θ23. This scheme predicts sin θ13 = 0.149, which is almost equal to the latest best fit, as a function of the lepton masses me, μ and the mass differences $\Delta m_{i1}^{2}$. Moreover, even if the mass matrix has perturbations that break the magic symmetry, the prediction of sin θ13 is retained with good accuracy for the four-zero texture with diagonal reflection symmetries.