Lepton masses and mixings, and muon anomalous magnetic moment in an extended $B-L$ model with type I seesaw mechanism

We propose a $B-L$ model combined with the $S_4\times Z_3\times Z_4$ discrete symmetry which successfully explains the recent $3+1$ sterile - active neutrino data. The smallness of neutrino mass is obtained through the type-I seesaw mechanism. The active-active and sterile-active neutrino mixing angles are predicted to be consistent with the recent constraints in which $0.3401(0.3402)\le {\sin }^2{\theta }_{12}\le 0.3415(0.3416),0.456(0.433)\le {\sin }^2{\theta }_{23}\le 0.544(0.545),2.00(2.018)\le {10}^2\times {\sin }^2{\theta }_{13}\le 2.405(2.424),156(140.8)\le {\delta }_{CP}^{(\circ )}\le 172(167.2)$ for normal (inverted) ordering of the three neutrino scenario, and $0.015(0.022)\le s_{14}^2\le 0.045(0.029),0.005(0.0095)\le s_{24}^2\le 0.012(0.012),0.003(0.009)\le s_{34}^2\le 0.011$ for normal (inverted) ordering of the $3+1$ neutrino scenario. Our model predicts flavour conserving leptonic neutral scalar interactions and successfully explains the muon $g-2$ anomaly.