Charged Fermion Masses and Mixing from a SU(3) Family Symmetry Model

Abstract

Within the framework of a Beyond Standard Model (BSM) with a local $SU(3)$ family symmetry, we report an updated fit of parameters which account for the known spectrum of quarks and charged lepton masses and the quark mixing in a $4\times 4$ non-unitary $V_{CKM}$. 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 See-saw Majorana neutrino mass matrix with four massless eigenvalues at tree level. Hence, light fermions, including neutrinos, obtain masses from loop radiative corrections mediated by the massive $SU(3)$ gauge bosons. $SU(3)$ family symmetry is broken spontaneously in two stages, whose hierarchy of scales yield an approximate $SU(2)$ global symmetry associated with the $Z_1,Y_1^{\pm }$ gauge boson masses of the order of 2 TeV. A global fit of parameters to include neutrino masses and lepton mixing is in progress.

Comments: LaTex 14 pages, 1 figure. Contribution to Proceedings to the 18th Bled workshop "What comes beyond the standard models.", 11-19 July, 2015, Bled, Slovenia. version with minor improvements and corrections. arXiv admin note: substantial text overlap with arXiv:1212.4571, arXiv:1312.3403