Limits on doubly charged Higgs bosons and lepton-flavor violation

We consider the effect of a doubly charged Higgs boson (${\Delta }^{--}$) on several processes. We find that the effective Hamiltonian that is normally used to interpret the results of muonium-antimuonium oscillation experiments also describes the $t$-channel exchange of a ${\Delta }^{--}$. A limit on the existence of the ${\Delta }^{--}$ is extracted from the most recent muonium oscillation result. The effect of ${\Delta }^{--}$ exchange on high-energy Bhabha scattering is discussed, and a limit is extracted from the published cross sections of several experiments at the SLAC and DESY storage rings PEP and PETRA. The case of a nondiagonal coupling of the ${\Delta }^{--}$ to the charged leptons (nondiagonal in lepton flavor) is considered. A limit is extracted from the result of the most recent search for the rare decay $\mu \to 3e$. Finally, a coupling-independent limit is extracted from a recent measurement of the process $e^{+}{e}^{-}\to 4 \mathrm{leptons}$ at PETRA.