Fermion mass and mixing in the $U{\left(1\right)}_{B-L}$ extension of the standard model with D₄ symmetry

We propose a renormalizable B − L standard model extension based on D ₄ symmetry which accommodates fermion mass and mixing parameters with CP violation. Both normal and inverted neutrino mass ordering as well as the smallness of the active neutrino masses are generated through a type I seesaw mechanism. The obtained physical parameters are well consistent with the global fit of neutrino oscillation in Esteban et al (2019 J. High Energy Phys. JHEP01(2019)106) while the quark masses are in good agreement with the recent experimental data (Tanabashi et al (Particle Data Group) 2018 Phys. Rev. D 98 030001 and 2019 update). The model also predicts an effective neutrino mass parameter of $⟨m_{ee}⟩=1.24\times {10}^{-2}eV$ for normal hierarchy and $⟨m_{ee}⟩=4.88\times {10}^{-2}eV$ for inverted hierarchy which are all consistent with the recent experimental limits on neutrinoless double beta decay. (paper)