Predictions for the neutrino parameters in the minimal gauged U(1)Lμ-Lτ model

Abstract

We study the structure of the neutrino-mass matrix in the minimal gauged U(1)Lμ-Lτ model, where three right-handed neutrinos are added to the Standard Model in order to obtain non-zero masses for the active neutrinos. Because of the U(1)Lμ-Lτ gauge symmetry, the structure of both Dirac and Majorana mass terms of neutrinos is tightly restricted. In particular, the inverse of the neutrino-mass matrix has zeros in the (μ, μ) and (τ, τ) components, namely, this model offers a symmetric realization of the so-called two-zero-minor structure in the neutrino-mass matrix. Due to these constraints, all the CP phases – the Dirac CP phase δ and the Majorana CP phases α2 and α3 – as well as the mass eigenvalues of the light neutrinos mi are uniquely determined as functions of the neutrino mixing angles θ12, θ23, and θ13, and the squared mass differences Δm212 and Δm312. We find that this model predicts the Dirac CP phase δ to be δ≃ 1.59 π–1.70 π (1.54 π–1.78 π), the sum of the neutrino masses to be ∑ imi≃ 0.14 –0.22 eV (0.12–0.40 eV), and the effective mass for the neutrinoless double-beta decay to be ⟨ mββ⟩ ≃ 0.024 –0.055 eV (0.017–0.12 eV) at 1 σ (2 σ) level, which are totally consistent with the current experimental limits. These predictions can soon be tested in future neutrino experiments. Implications for leptogenesis are also discussed.