Model for the dynamical generation of lepton, quark, and intermediate-boson masses.

Abstract

In an SU(3${)}_{\mathrm{c}}$\ifmmode\times\else\texttimes\fi{}SU(2${)}_{\mathrm{L}}$\ifmmode\times\else\texttimes\fi{}U(1${)}_{\mathrm{Y}}$ gauge-invariant model without the Higgs sector the fermions are distinguished by different hypercharges of a new renormalizable interaction with an ``Abelian'' vector boson C of mass M. An interplay of all interactions which contribute to the fermion mass generation yields the fermion mass formulas ${\mathit{m}}_{\mathit{i}}$(l)=M exp [-\ensuremath{\pi}/3\ensuremath{\alpha}'(${\mathrm{\ensuremath{\mu}}}_{\mathit{i}}$)], ${\mathit{m}}_{\mathit{i}}$(u)=M exp{-\ensuremath{\pi}/[2${\mathrm{\ensuremath{\alpha}}}_{\mathit{s}}$(${\mathrm{\ensuremath{\mu}}}_{\mathit{i}}$)+2/3\ensuremath{\alpha}'(${\mathrm{\ensuremath{\mu}}}_{\mathit{i}}$)]}, and ${\mathit{m}}_{\mathit{i}}$(d)=M exp{-\ensuremath{\pi}/[2${\mathrm{\ensuremath{\alpha}}}_{\mathit{s}}$(${\mathrm{\ensuremath{\mu}}}_{\mathit{i}}$)-1/3\ensuremath{\alpha}'(${\mathrm{\ensuremath{\mu}}}_{\mathit{i}}$)]} for the charged leptons ${\mathit{l}}_{\mathit{i}}$, ${\mathit{u}}_{\mathit{i}}$, and ${\mathit{d}}_{\mathit{i}}$ quarks, respectively. Here \ensuremath{\alpha}' and ${\mathrm{\ensuremath{\alpha}}}_{\mathit{s}}$ are the running coupling strengths of the U(1${)}_{\mathrm{Y}}$ and SU(3${)}_{\mathrm{c}}$ gauge interactions, respectively, and ${\ensuremath{\mu}}_{i}$ are the physically preferred renormalization points determined by the C hypercharges. The intermediate-boson masses ${m}_{W}$ and ${m}_{Z}$ are expressed in terms of the fermion masses by sum rules.