3+1$$ 3 + 1 active–sterile neutrino mixing in $$B-L$$ B - L model with $$S_{3}{\times Z_4\times Z_2}$$ S 3 × Z 4 × Z 2 symmetry for normal neutrino mass ordering

Abstract We propose a non-renormalizable $$B-L$$ B - L model with $$S_{3}{\times Z_4\times Z_2}$$ S 3 × Z 4 × Z 2 symmetry which successfully accommodates the current active–sterile neutrino mixing in $$3+1$$ 3 + 1 scheme. The $$S_3$$ S 3 flavor symmetry is supplemented by $$Z_4\otimes Z_2$$ Z 4 ⊗ Z 2 symmetry to consolidate the Yukawa interaction of the model. The presence of $$S_3\otimes Z_4\otimes Z_2$$ S 3 ⊗ Z 4 ⊗ Z 2 flavour symmetry plays an important role in generating the desired structure of the neutrino mass matrix. The model can reproduce the recent observed active-neutrino neutrino oscillation data for normal ordering in which two sterile–active mixing angles $$\theta _{14, 24}$$ θ 14 , 24 get the best-fit values and the obtained values of $$\theta _{34}, \delta _{14}, \delta _{14}$$ θ 34 , δ 14 , δ 14 , the sum of neutrino mass and the effective neutrino masses are within their currently allowed ranges.