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 $\tan\beta \equiv |v_2|/|v_1| \sim 1$, contributions from two loop diagrams involving the $t$ quark and the $W$ boson dominate; while for $\tan\beta \gsim 10$, contributions from two loop diagrams involving the $b$ quark and the $\tau$ lepton are dominant. For $8 \gsim \tan\beta \gsim 4$, significant cancellation occurs among the contributions from two loop diagrams and the one loop contribution dominates for $\tan\beta \sim 7$. For $\tan\beta \gsim 15$, the calculated $d_\mu$ can be close to the reach of a recently proposed experiment at the Brookhaven National Laboratory.