The Muon Electric Dipole Moment

The electric dipole moment of the muon ($d_{\mu }$) is evaluated in a two Higgs doublet model with a softly broken discrete symmetry. For $\tan\beta \equiv |v_2|/|v_1| \sim 1$,contributionsfromtwoloopdiagramsinvolvingthe$t$quarkandthe$W$bosondominate;whilefor$\tan\beta \gsim 10$, contributions from two loop diagrams involving the $b$ quark and the $\tau$ lepton are dominant. For $8\text{gsim}\tan \beta \text{gsim}4$, significant cancellation occurs among the contributions from two loop diagrams and the one loop contribution dominates for $\tan \beta \sim 7$. For $\tan \beta \text{gsim}15$, the calculated $d_{\mu }$ can be close to the reach of a recently proposed experiment at the Brookhaven National Laboratory.