Supersymmetric Relations Among Electromagnetic Dipole Operators

Supersymmetric contributions to all leptonic electromagnetic dipole operators have essentially identical diagramatic structure. With approximate slepton universality this allows the muon anomalous magnetic moment to be related to the electron electric dipole moment in terms of supersymmetric phases, and to radiative flavor changing lepton decays in terms of small violations of slepton universality. If the current discrepancy between the measured and Standard Model values of the muon anomalous magnetic moment is due to supersymmetry, the current bound on the electron electric dipole moment then implies that the phase of the electric dipole operator is less than $2 \times 10^{-3}$. Likewise the current bound on $\mu \to e \gamma$ decay implies that the fractional selectron-smuon mixing in the left-left mass squared matrix, $\delta m_{\smuon \selectron}^2 / m_{\slepton}^2$, is less than $10^{-4}$. These relations and constraints are fairly insensitive to details of the superpartner spectrum for moderate to large $\tan \beta$.