Neutrino Mass, Muon Anomalous Magnetic Moment, and Lepton Flavor Nonconservation

If the generating mechanism for neutrino mass is to account for both the newly observed muon anomalous magnetic moment as well as the present experimental bounds on lepton flavor nonconservation, then the neutrino mass matrix should be almost degenerate and the underlying physics be observable at future colliders. We illustrate this assertion in two specific examples, and show that $\Gamma (\mu \to e \gamma)/m_\mu^5$, $\Gamma (\tau \to e \gamma)/m_\tau^5$, and $\Gamma (\tau \to \mu \gamma) /m_\tau^5$ are in the ratio $(\Delta m^2)_{sol}^2/2$, $(\Delta m^2)_{sol}^2 /2$, and $(\Delta m^2)_{atm}^2$ respectively, where the $\Delta m^2$ parameters are those of solar and atmospheric neutrino oscillations and bimaximal mixing has been assumed.