$$U(1)_{B-L}$$ U(1)B-L extension of the standard model with $$S_3$$ S3 symmetry

Abstract

Abstract We propose a renormalizable $$B-L$$ B-L Standard Model (SM) extension based on $$S_3$$ S3 symmetry which successfully accommodates the observed fermion mass spectra and flavor mixing patterns as well as the CP violating phases. The small masses for the light active neutrinos are generated through a type I seesaw mechanism. The obtained physical parameters in the lepton sector are well consistent with the global fit of neutrino oscillations (Esteban et al. in J High Energy Phys 01:106, 2019) for both normal and inverted neutrino mass orderings. The model also predicts effective neutrino mass parameters of $${\langle m_{ee}\rangle }= {1.02\times 10^{-2}}\,{\mathrm {eV}},\, m_{\beta }= {1.25}\times 10^{-2}\,{\mathrm {eV}}$$ ⟨mee⟩=1.02×10-2eV,mβ=1.25×10-2eV for normal hierarchy (NH) and $${\langle m_{ee}\rangle } ={5.03}\times 10^{-2}\, {\mathrm {eV}},\, m_{\beta } ={5.05}\times 10^{-2}\, {\mathrm {eV}}$$ ⟨mee⟩=5.03×10-2eV,mβ=5.05×10-2eV for inverted hierarchy (IH) which are all well consistent with the future large and ultra-low background liquid scintillator detectors which has been discussed in Ref. (Zhao et al. in Chin Phys C 41(5):053001, 2017) or the limit of the effective neutrino mass can be reached by the planning of future experiments. The model results are consistent with and successfully accommodate the recent experimental values of the physical observables of the quark sector, including the six quark masses, the quark mixing angles and the CP violating phase in the quark sector.