Predictions for the neutrino parameters in the minimal gauged U(1)${}_{L_{\mu }-L_{\tau }}$ model

Abstract

We study the structure of the neutrino mass matrix in the minimal gauged U(1)${}_{L_{\mu }-L_{\tau }}$ 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)${}_{L_{\mu }-L_{\tau }}$ 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 $(\mu ,\mu )$ and $(\tau ,\tau )$ 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 $\delta$ and the Majorana CP phases ${\alpha }_2$ and ${\alpha }_3$-as well as the mass eigenvalues of the light neutrinos $m_i$ are uniquely determined as functions of the neutrino mixing angles ${\theta }_{12}$, ${\theta }_{23}$, and ${\theta }_{13}$, and the squared mass differences $\Delta m_{21}^2$ and $\Delta m_{31}^2$. We find that this model predicts the Dirac CP phase $\delta$ to be $\delta \simeq 1.59\pi$-$1.70\pi$ ($1.54\pi$-$1.78\pi$), 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 $⟨m_{\beta \beta }⟩\simeq 0.024$-0.055 eV ($0.017$-0.12 eV) at $1\sigma$ ($2\sigma$) 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.

Comments: v1: 23 pages, 6 figures. v2: 24 pages, 8 figures, Discussion on leptogenesis added