Charged lepton and Neutrino masses from a low energy SU(3) flavour symmetry model

Abstract: We report a recent study on lepton masses within a beyond standard model with a SU(3) family symmetry model. 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. 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. Recent analysis shows the existence of a space parameter region where the $M_U, M_D,M_E,M_N$ vector-like fermion masses are within a scale of a few TeV's. 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. We report a preliminary solution for ordinary charged lepton masses $(m_e, m_\mu, m_\tau) = (0.486, 102.7, 1746.17) MeV$ at the $M_Z$ scale, a $M_E \approx 2.6 TeV$ and SU(3) gauge boson masses of $\mathcal{O} (10 TeV)$. A detailed numerical analysis on neutrino masses and mixing is in progress and hopefully shall be reported soon.