Limit on the electric charge-nonconserving $\mu^+ \to invisible$ decay

The first limit on the branching ratio of the electric charge-nonconserving invisible muon decay $Br(\mu^+ \to invisible) < 5.2 \times 10^{-3}$ is obtained from the recently reported results on new determination of the Fermi constant from muon decays. The results of a feasibility study of a new proposed experiment for a sensitive search for this decay mode at the level of a few parts in 10^{11} are presented. Constrains on the $\tau \to invisible$ decay rate are discussed. These leptonic charge-nonconserving processes may hold in four-dimensional world in models with infinite extra dimensions, thus making their searches complementary to collider experiments probing new physics.