$B-L$ model with $A_4\times Z_3\times Z_4$ symmetry for $3+1$ active$-$sterile neutrino mixing

Abstract

We construct a multiscalar and nonrenormalizable $B-L$ model with $A_4\times Z_3\times Z_4$ flavor symmetry which successfully explains the recent $3+1$ active-sterile neutrino data. The tiny neutrino mass the mass hierarchy are obtained by the type-I seesaw mechanism. The hierarchy of the lepton masses is satisfied by a factor of $v_H{\left(\frac{v_l}{\Lambda }\right)}^2\sim 10^{-4}\mathrm{GeV}$ of the electron mass compared to the muon and tau masses of the order of $\frac{v_H{v}_l}{\Lambda }\sim 10^{-1}\mathrm{GeV}$. The recent $3+1$ active-sterile neutrino mixings are predicted to be $0.015\le |U_{e4}{|}^2\le 0.045$, $0.004\le |U_{\mu 4}{|}^2\le 0.012$, $0.004\le |U_{\tau 4}{|}^2\le 0.014$ for normal hierarchy and $0.020\le |U_{e4}{|}^2\le 0.045$, $0.008\le |U_{\mu 4}{|}^2\le 0.018$, $0.008\le |U_{\tau 4}{|}^2\le 0.022$ for inverted hierarchy. Sterile neutrino masses are predicted to be $0.7\lesssim m_s(\mathrm{eV})\lesssim 3.16$ for normal hierarchy and $2.6\lesssim m_s(\mathrm{eV})\lesssim 7.1$ for inverted hierarchy. For three neutrino scheme the model predicts $0.3401\le {\sin }^2{\theta }_{12}\le 0.3415,0.460\le {\sin }^2{\theta }_{23}\le 0.540,-0.60\le \sin {\delta }_{CP}\le -0.20$ for normal hierarchy and $0.3402\le {\sin }^2{\theta }_{12}\le 0.3416,0.434\le {\sin }^2{\theta }_{23}\le 0.610,-0.95\le \sin {\delta }_{CP}\le -0.60$ for inverted hierarchy. The effective neutrino masses are predicted to be $35.70 \leq \langle m_{ee}\rangle [\mbox{meV}] \leq 36.50$ in 3+1 scheme and $3.65 \leq \langle m^{(3)}_{ee}\rangle [\mbox{meV}] \leq 4.10$ in three neutrino scheme for NH while $160.0 \leq \langle m_{ee}\rangle [\mbox{meV}] \leq 168.0$ in 3+1 scheme and $47.80 \leq \langle m^{(3)}_{ee}\rangle [\mbox{meV}] \leq 48.70$ in three neutrino scheme for for IH which are all in agreement with the recent experimental data.

33 pages, 12 figures, 4 tables

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• Neutrino phenomenology and keV dark matter in 2HDM with $A_4$ symmetry