Slepton flavor nonuniversality, the muon electric dipole moment, and its proposed sensitive search at Brookhaven

We analyze the electric dipole moment of the electron ${(d}_e),$ of the neutron ${(d}_n),$ and of the muon ${(d}_{\mu }),$ using the cancellation mechanism in the presence of nonuniversalities of the soft breaking parameters. It is shown that the nonuniversalities in the slepton sector produce a strong violation of the scaling relation $d_{\mu }{/d}_e\simeq m_{\mu }{/m}_e$ in the cancellation region. An analysis of $d_e,$ $d_n,$ and $d_{\mu }$ under the constraints of the current experimental limits on $d_e$ and $d_n,$ and under the constraints of the recent Brookhaven result on $g_{\mu }-2,$ shows that in the nonscaling region, $d_{\mu }$ can be as large as ${(10\mathrm{}}^{-24}-{10}^{-23})e\mathrm{cm}$ and thus within reach of the recently proposed Brookhaven experiment for a sensitive search for $d_{\mu }$ at the level of ${10}^{-24}e\mathrm{cm}.$