Search for lepton-number- and baryon-number-violating tau decays at Belle

We search for lepton-number- and baryon-number-violating decays $τ^{-}\to\overline{p}e^{+}e^{-}$, $pe^{-}e^{-}$, $\overline{p}e^{+}μ^{-}$, $\overline{p}e^{-}μ^{+}$, $\overline{p}μ^{+}μ^{-}$, and $pμ^{-}μ^{-}$ using 921 fb$^{-1}$ of data, equivalent to $(841\pm12)\times 10^6$ $τ^{+}τ^{-}$ events, recorded with the Belle detector at the KEKB asymmetric-energy $e^{+}e^{-}$ collider. In the absence of a signal, $90\%$ confidence-level upper limits are set on the branching fractions of these decays in the range $(1.8$-$4.0)\times 10^{-8}$. We set the world's first limits on the first four channels and improve the existing limits by an order of magnitude for the last two channels.