Weak scale radiative lepton mass.

Abstract

We construct a ${\mathit{Z}}_{8}$ model for leptons where all Yukawa couplings are of order unity, but known lepton masses are generated radiatively, order by order. The seed is provided by fourth generation leptons E and N, and two additional Higgs doublets are introduced to give nearest-neighbor Yukawa couplings. Loop masses are generated when ${\mathit{Z}}_{8}$ is softly broken down to ${\mathit{Z}}_{2}$, while ${\mathit{m}}_{\mathit{e}}$ and ${\mathit{m}}_{\mathrm{\ensuremath{\mu}}}$ generation require Higgs bosons to be weak scale. The ${\mathit{Z}}_{2}$ symmetry forbids \ensuremath{\mu}\ensuremath{\rightarrow}e\ensuremath{\gamma}. The most stringent bound comes from \ensuremath{\tau}\ensuremath{\rightarrow}\ensuremath{\mu}${\mathrm{\ensuremath{\mu}}}^{\ifmmode\pm\else\textpm\fi{}}$${\mathit{e}}^{\ensuremath{\mp}}$. The model has implications for \ensuremath{\tau}\ensuremath{\rightarrow}e\ensuremath{\gamma}, \ensuremath{\mu}e\ifmmode\bar\else\textasciimacron\fi{}\ensuremath{\rightarrow}\ensuremath{\mu}\ifmmode\bar\else\textasciimacron\fi{}e conversion, \ensuremath{\mu}\ensuremath{\rightarrow}e${\ensuremath{\nu}}_{\mathit{e}}$\ensuremath{\nu}${\mathrm{\ifmmode\bar\else\textasciimacron\fi{}}}_{\mathrm{\ensuremath{\mu}}}$, and FCNC decays of E and N (such as E\ensuremath{\rightarrow}\ensuremath{\tau}${\mathit{e}}^{\ifmmode\pm\else\textpm\fi{}}$${\mathrm{\ensuremath{\mu}}}^{\ensuremath{\mp}}$).