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Within the framework of a local SU(3) family symmetry model, we report ageneral analysis of the mechanism for neutrino mass generation and mixing,including light sterile neutrinos. In this scenario, ordinary heavy fermions,top and bottom quarks and tau lepton, become massive at tree level from DiracSee-saw mechanisms implemented by the introduction of a new set of $SU(2)_L$weak singlet vector-like fermions, U,D,E,N, with N a sterile neutrino.Right-handed and the $N_{L,R}$ sterile neutrinos allow the implementation of a8x8 general Majorana neutrino mass matrix with four or five massless neutrinosat tree level. Hence, light fermions, including light neutrinos get masses fromradiative corrections mediated by the massive SU(3) gauge bosons. We report thecorresponding Majorana neutrino mass matrix up to one loop. Previous numericalanalysis of the free parameters show out solutions for quarks and chargedlepton masses within a parameter space region where the vector-like fermionmasses $M_U, M_D, M_E$, and the SU(3) family gauge boson masses lie in the lowenergy region of $\mathcal{O} (1-20)\,$TeV, with light neutrinos within thecorrect order of square neutrino mass differences: $m_2^2-m_1^2 \approx 7\times 10^{-5}\;\text{eV}^2$, $m_3^2-m_1^2 \approx 2 \times10^{-3}\;\text{eV}^2$, and at least one sterile neutrino of the order $\approx0.5\;\text{eV}$. A more precise fit of the parameters is still needed toaccount also for the quark and lepton mixing.

General Majorana Neutrino Mass Matrix from a Low Energy SU(3) Family Symmetry with Sterile Neutrinos