  Within the framework of a local SU(3) family symmetry model, we report a
general 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 Dirac
See-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 a
8x8 general Majorana neutrino mass matrix with four or five massless neutrinos
at tree level. Hence, light fermions, including light neutrinos get masses from
radiative corrections mediated by the massive SU(3) gauge bosons. We report the
corresponding Majorana neutrino mass matrix up to one loop. Previous numerical
analysis of the free parameters show out solutions for quarks and charged
lepton masses within a parameter space region where the vector-like fermion
masses $M_U, M_D, M_E$, and the SU(3) family gauge boson masses lie in the low
energy region of $\mathcal{O} (1-20)\,$TeV, with light neutrinos within the
correct order of square neutrino mass differences: $m_2^2-m_1^2 \approx 7
\times 10^{-5}\;\text{eV}^2$, $m_3^2-m_1^2 \approx 2 \times
10^{-3}\;\text{eV}^2$, and at least one sterile neutrino of the order $\approx
0.5\;\text{eV}$. A more precise fit of the parameters is still needed to
account also for the quark and lepton mixing.
