Probing Lepton Flavor Violation at Future Colliders

Supersymmetric theories with significant lepton flavor violation have $\tilde{e}$ and $\tilde{\mu }$ nearly degenerate. In this case, pair production of ${\tilde{e}}^{+}{\tilde{e}}^{-}$ and ${\tilde{\mu }}^{+}{\tilde{\mu }}^{-}$ at LEP II and at the Next Linear Collider (NLC) leads to the phenomenon of slepton oscillations, which is analogous to neutrino oscillations. The reach in $\Delta m^2$ and ${sin}^{2}2\theta$ gives a probe of lepton flavor violation which is significantly more powerful than the current bounds from rare processes, such as $\mu \to e\gamma$. Polarizable $e^{-}$ beams and the $e^{-}{e}^{-}$ mode at the NLC are found to be promising options.