Quark and lepton masses and mixing from a gauged $SU(3)_$F family symmetry with a light $\mathcal[O}$(eV) sterile Dirac neutrino

International audienceIn the framework of a complete vector-like and universal gauged SU(3) F familysymmetry, we report a global region in the parameter space where this approachcan account for a realistic spectrum of quark masses and mixing in a 4 × 4 non-unitary V CKM , as well as for the known charged lepton masses and the squaredneutrino mass differences reported from neutrino oscillation experiments. TheSU(3) F family symmetry is broken spontaneously in two stages by heavy SMsinglet scalars, whose hierarchy of scales yield and approximate SU(2) F globalsymmetry associated to the almost degenerate boson masses of the order of thelower scale of the SU(3) F SSB. The gauge symmetry, the fermion content, and thetransformation of the scalar fields, all together, avoid Yukawa couplingsbetween SM fermions. Therefore, in this scenario ordinary heavy fermions, topand bottom quarks and tau lepton, become massive at tree level from Dirac Seesawmechanisms, while light fermions, including light neutrinos, obtain masses fromradiative corrections mediated by the massive gauge bosons of the SU(3) F familysymmetry. The displayed fit parameter space region solution for fermion massesand mixing yield the vector-like fermion masses: M D ≈ 3.2 TeV, M U ≈ 6.9 TeV, ME ≈ 21.6 TeV, SU(2) F family gauge boson masses of O(2 TeV), and the squaredneutrino mass differences: m 2 2 − m 2 1 ≈ 7.5 × 10 −5 eV 2 , m 2 3 − m 2 2 ≈2.2 × 10 −3 eV 2 , m 2 4 − m 2 1 ≈ 0.81 eV 2. Povzetek. Avtor ponudi razširitevstandardnega modela, ki k poznanim grupam dodašedodaˇdodaše družinsko(umeritveno) grupo SU(3) F. Poišče območje v prostoru parametrov, ki ponudieksperimentalno sprejemljive lastnosti kvarkov in leptonov. Družinsko simetrijozlomi v dveh korakih. Težki fermioni-kvarka t in b ter lepton tau-postanejomasivni na drevesnem nivoju (z mehanizmom gugalnice, seesaw), ostali pa spopravki višjih re-dov. Mase fermionov, pri katerih sokvantnaštevilakvantnaˇkvantnaštevila levoročnih in desnoročnih fermionov enaka,so nekaj TeV ali več: M D ≈ 3.2 TeV, M U ≈ 6.9 TeV, M E ≈ 21.6 TeV. Mase bo-zonov z družinskimi kvantnimištevilikvantnimiˇkvantnimištevili so O(2 TeV),razliki kvadratov nevtrinskih mass pa so:m 2 2 − m 2 1 ≈ 7.5 × 10 −5 eV 2 , m 23 − m 2 2 ≈ 2.2 × 10 −3 eV 2 , m 2 4 − m 2 1 ≈ 0.81 eV 2