We construct extended Higgs-boson models of soft CP-invariance violation arising from scalar-pseudoscalar mixing. Using the electric dipole moment of neutron as input, we find that the charged-lepton electric dipole moments scale as (mass${)}^{3}$. They are estimated to be 2.1\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}28}$, 4.4\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}22}$, and 1.8\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}19}$ e cm for electron, muon, and \ensuremath{\tau}, respectively. An important test of this source of CP violation lies in the longitudinal polarizations of muon in \ensuremath{\eta}\ensuremath{\rightarrow}\ensuremath{\mu}\ensuremath{\mu}\ifmmode\bar\else\textasciimacron\fi{} and ${K}_{L}^{0}$\ensuremath{\rightarrow}\ensuremath{\mu}\ensuremath{\mu}\ifmmode\bar\else\textasciimacron\fi{}, which we estimate to be of the order of ${10}^{\mathrm{\ensuremath{-}}2}$ and ${10}^{\mathrm{\ensuremath{-}}1}$, respectively.
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