Predictions for the neutrino parameters in the minimal gauged U(1)$_{L_μ-L_τ}$ model

Abstract

We study the structure of the neutrino mass matrix in the minimal gauged U(1)$_{L_μ-L_τ}$ model, where three right-handed neutrinos are added to the Standard Model in order to obtain non-zero masses for active neutrinos. Because of the U(1)$_{L_μ-L_τ}$ 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 $α_2$ and $α_3$-as well as the mass eigenvalues of the light neutrinos $m_i$ are uniquely determined as functions of the neutrino mixing angles $θ_{12}$, $θ_{23}$, and $θ_{13}$, and the squared mass differences $Δm_{21}^2$ and $Δm_{31}^2$. We find that this model predicts the Dirac CP phase $δ$ to be $δ\simeq 1.59π$-$1.70π$ ($1.54π$-$1.78π$), the sum of the neutrino masses to be $\sum_{i}m_i \simeq 0.14$-0.22 eV ($0.12$-0.40 eV), and the effective mass for the neutrinoless double beta decay to be $\langle m_{ββ}\rangle \simeq 0.024$-0.055 eV ($0.017$-0.12 eV) at $1σ$ ($2σ$) 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.