Neutrino masses and mixing within a SU(3) family symmetry model with one or two light sterile neutrinos

Abstract

We report a global fit of parameters for fermion masses and mixing, including light sterile neutrinos, within a local vector $SU(3)$ family symmetry model. In this scenario, ordinary heavy fermions, top and bottom quarks and tau lepton, become massive at tree level from {\bf 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. The $N_{L,R}$ sterile neutrinos allow the implementation of a $8\times 8$ general tree level See-saw Majorana neutrino mass matrix with four massless eigenvalues. Hence, light fermions, including light neutrinos obtain masses from one loop radiative corrections mediated by the massive $SU(3)$ gauge bosons. This BSM model is able to accommodate the known spectrum of quark masses and mixing in a $4\times 4$ non-unitary $V_{CKM}$ as well as the charged lepton masses. The explored parameter space region provide the vector-like fermion masses: $M_D\approx 914.365$GeV, $M_U\approx 1.5$TeV, $M_E\approx 5.97$TeV, $SU(3)$ family gauge boson masses of $\mathcal{O}(1-10)$TeV, the neutrino masses $(m_1,m_2,m_3,m_4,m_5,m_6,m_7,m_8)=(0,0.0085,0.049,0.22,3.21,1749.96,1\times 10^8,1\times 10^9)$eV, with the squared neutrino mass differences: $m_2^2-m_1^2\approx 7.23\times 10^{-5}{\text{eV}}^2$, $m_3^2-m_1^2\approx 2.4\times 10^{-3}{\text{eV}}^2$, $m_4^2-m_1^2\approx 0.049{\text{eV}}^2$, $m_5^2-m_1^2\approx 10.3{\text{eV}}^2$. We also show the corresponding $U_{PMNS}$ lepton mixing matrix. However, the neutrino mixing angles are extremely sensitive to parameter space region, and an improved and detailed analysis is in progress.

Comments: LaTex 20 pages, 3 figures. To appear in the Proceedings to the 16th Workshop "What Comes Beyond the Standard Models", 14-21 July, Bled, Slovenia