On the Origin of Lepton and Quark Masses

Abstract

Gauging the flavor (family, generation, horizontal) index of the chiral fermion fields of the Standard model, for anomaly freedom extended by three sterile right-handed neutrino fields, results in asymptotically free, {\it bona fide} nonconfining $SU(3)_f$ quantum flavor dynamics. Approximate nonperturbative strong-coupling solutions of the corresponding Schwinger-Dyson (SD) equation for fermion self-energies give rise to the complete flavor symmetry breaking by : (1) Three huge Majorana masses of sterile right-handed neutrinos. (2) Three exponentially light Dirac masses common to all fermion sorts in a family. Masses of charged leptons and quarks are further distinguished from Dirac neutrino masses by the weak hypercharge contributions to the universal $SU(3)_f$ kernel of the SD equation, free of unknown parameters. The $SU(3)_f$ dynamics itself thus gives the neutrino mass spectrum in the seesaw form.