Lepton masses and SU(3)family-symmetry breaking

If it is assumed, among the technicolored SU(3${)}_{\mathrm{family}}$ 8+1 bosons, that only the lowest-lying and particularly mixed single boson contributes to the lepton mass-generation mechanism, a very successful prediction on the τ lepton mass, $m_{\tau }$=1.787 GeV, can be obtained from the input data $m_e$ and $m_{\mu }$. A possible simple scenario for the mass-splitting pattern of the 8+1 bosons, which can realize this particular 8+1 mixing, is investigated by assuming that the broken SU(3${)}_{\mathrm{family}}$ symmetry satisfies asymptotic symmetry. In this scenario, though small, ${\tau }^{+}$ ${\tau }^{\mathrm{-}}$ excess in the bottomonium and toponium decays into lepton pairs may be expected.