Quark and lepton masses and mixing from a gauged SU(3)_F family symmetry with a light O(eV) sterile Dirac neutrino

Abstract: In the framework of a complete vector-like and universal gauged SU(3)F family symmetry, we report a global region in the parameter space where this approach can account for a realistic spectrum of quark masses and mixing in a 4 x 4 non-unitary V{CKM}, as well as for the known charged lepton masses and the squared neutrino mass differences reported from neutrino oscillation experiments. The $SU(3)_F$ family symmetry is broken spontaneously in two stages by heavy SM singlet scalars, whose hierarchy of scales yield and approximate SU(2)_F global symmetry associated to the almost degenerate boson masses of the order of the lower scale of the SU(3)_F SSB. The gauge symmetry, the fermion content, and the transformation of the scalar fields, all together, avoid Yukawa couplings between SM fermions. Therefore, in this scenario ordinary heavy fermions, top and bottom quarks and tau lepton, become massive at tree level from Dirac See-saw mechanisms, while light fermions, including light neutrinos, obtain masses from radiative corrections mediated by the massive gauge bosons of the SU(3)_F family symmetry. The displayed fit parameter space region solution for fermion masses and mixing yield the vector-like fermion masses: M_D \approx 3.2 \,TeV, M_U \approx 6.9 \,TeV, M_E \approx 21.6 \,TeV, SU(2)_F family gauge boson masses of $\mathcal{O} (2 TeV)$, and the squared neutrino mass differences: m_2^2-m_1^2 \approx 7.5 x 10^{-5}\;eV^2, m_3^2-m_2^2 \approx 2.2 x 10^{-3}\;eV^2, m_4^2-m_1^2 \approx 0.82\;eV^2.