One-prong $\tau$ decays with kaons

One-prong $\tau$ decays into final states involving kaons are studied with about 161k $\tau^+\tau^-$ events collected by the ALEPH detector from 1991 to 1995. Charged kaons are identified by dE/dx measurement, while $K^0_L$'s are detected through their interaction in calorimeters. Branching ratios are measured for the inclusive mode, $B(\tau^-\rightarrow K^-X\nu_\tau)=(1.52 \pm 0.04\pm0.04)\%$, where $X$ can be any system of neutral particles, and for the exclusive modes \begin{center} \begin{tabular}{rcl} $B(\tau^-\to K^-\nu_\tau)$ &=& $(6.96\pm0.25\pm0.14)\times 10^{-3}$,\\ $B(\tau^-\to K^-\pi^0\nu_\tau)$ &=& $(4.44\pm0.26\pm0.24)\times 10^{-3}$,\\ $B(\tau^-\to K^-\pi^0\pi^0\nu_\tau)$ &=& $(0.56\pm0.20\pm0.15)\times 10^{-3}$,\\ $B(\tau^-\to K^-\pi^0\pi^0\pi^0\nu_\tau)$ &=& $(0.37\pm0.21\pm0.11)\times 10^{-3}$,\\ $B(\tau^-\to K^-K^{0}\nu_\tau)$ &=& $(1.62\pm0.21\pm0.11)\ times 10^{-3}$,\\ $B(\tau^-\to K^{-}K^{0}\pi^0\nu_\tau)$ &