Experimental upper limits on branching fractions for unexpected decay modes of the $\tau$ lepton

Searches for 12 neutrinoless decay modes of the $\tau$ which violate lepton-number conservation have been made using the reaction $e^{+}{e}^{-}\to {\tau }^{+}{\tau }^{-}$. No evidence for lepton-number violation is observed, and we have set upper limits (90% C.L.) on the branching ratio for each decay mode. The branching-ratio limits on the radiative decays $\tau \to \mu \gamma$ and $\tau \to e\gamma$ are 0.055 and 0.064%, respectively. For the charged lepton decays $\tau \to \mathrm{eee}$, $\tau \to e\mu \mu$, $\tau \to \mu \mathrm{ee}$, and $\tau \to \mu \mu \mu$, the branching ratio limits are 0.040, 0.033, 0.044, and 0.049%, respectively. Upper limits on the branching ratios for the following charged lepton + neutral hadron decays are $\tau \to e{\rho }^0 \mathrm{}(0.037\%)\mathrm{}$, $\tau \to \mu {\rho }^0 \mathrm{}(0.044\%)\mathrm{}$, $\tau \to e{K}^0 \mathrm{}(0.13\%)\mathrm{}$, $\tau \to \mu K^0 \mathrm{}(0.10\%)\mathrm{}$, $\tau \to e{\pi }^0 \mathrm{}(0.21\%)\mathrm{}$, and $\tau \to \mu {\pi }^0 \mathrm{}(0.082\%)\mathrm{}$. We also use these data to search for the pair production in $e^{+}{e}^{-}$ annihilation of some unconventional particles with masses less than about 3 GeV/${\mathit{c}}^2$.