Predictions for the neutrino parameters in the minimal model extended by linear combination of U(1)$_{L_e-L_μ}$, U(1)$_{L_μ-L_τ}$ and U(1)$_{B-L}$ gauge symmetries

Abstract

We study the minimal extensions of the Standard Model by a linear combination of U(1)$_{L_e-L_μ}$, U(1)$_{L_μ-L_τ}$ and U(1)$_{B-L}$ gauge symmetries, where three right-handed neutrinos and one U(1)-breaking SU(2)$_L$ singlet or doublet scalar are introduced. Because of the dependence on the lepton flavor, the structures of both Dirac and Majorana mass matrices of neutrinos are restricted. In particular, the two-zero minor and texture structures in the mass matrix for the active neutrinos are interesting. Analyzing these structures, we obtain uniquely all the neutrino parameters, namely the Dirac CP phase $δ$, the Majorana CP phases $α_{2,3}$ and the mass eigenvalues of the light neutrinos $m_i$ as functions of the neutrino mixing angles $θ_{12}$, $θ_{23}$, and $θ_{13}$, and the squared mass differences $Δm^2_{21}$ and $Δm^2_{31}$. In 7 minimal models which are consistent with the recent neutrino oscillation data, we also obtain the predictions for the sum of the neutrino masses $Σ_i m_i$ and the effective Majorana neutrino mass $\langle m_{ββ} \rangle$ and compare them with the current experimental limits. In addition, we also discuss the implication of our results for leptogenesis.