Search for baryon and lepton number violating decays of the $\tau$ lepton

We have searched for five decay modes of the $\tau$ lepton that simultaneously violate lepton and baryon number: ${\tau }^{-}\to \overline{p}\gamma ,$ ${\tau }^{-}\to \overline{p}{\pi }^0,$ ${\tau }^{-}\to \overline{p}\eta ,$ ${\tau }^{-}\to \overline{p}2{\pi }^0,$ and ${\tau }^{-}\to \overline{p}{\pi }^0\eta .$ The data used in the search were collected with the CLEO II detector at the Cornell Electron Storage Ring. The integrated luminosity of the data sample is 4.7 ${\mathrm{fb}}^{-1},$ corresponding to the production of $4.3\times {10}^6\hspace{0.5em}{\tau }^{+}{\tau }^{-}$ events. No evidence is found for any of the decays, resulting in much improved upper limits on the branching fractions for the two-body decays and first upper limits for the three-body decays.