Three-prong $\tau$ decays with charged kaons

Final states with charged kaons in three-prong $\tau$ decays are studied by exploiting the particle identification from the dE/dx measurement. The results are based on a sample of about $1.6\times 10^{5}$ detected $\tau$ pairs collected with the ALEPH detector between 1991 and 1995 around the Z peak. The following branching ratios have been measured: $B(\tau^{-}~\rightarrow~K^{-}K^{+}\pi^{-}\nu_{\tau}) ~=~(1.63~\pm~0.21~\pm~0.17)~\times~10^{-3}$, $B(\tau^{-}~\rightarrow~K ^{-}\pi^{+}\pi^{-}\nu_{\tau}) ~=~(2.14~\pm~0.37~\pm~0.29)~\times~10^{- 3}$, $B(\tau^{-}~\rightarrow~K^{-}K^{+}\pi^{-}\pi^{0}\nu_{\tau})~=~$\\ $(0.75\pm~0.29\pm~0.15)\times~10^{-3}$, and $B(\tau^{-}\rightarrow K^{-}\pi^{+}\pi^{-}\pi^{0}\nu_{\tau}) =(0.61\pm~0.39\pm~0.18)\times~10^{-3}$. The first two measurements are more precise than the current world averages, while the last two channels are investigated for the first time. The $95\%$ C.L. upper limit on the branching ratio for the decay $\tau^{-}\rightarrow~K^{-}K^{+}K^{-}\nu_{\tau}$ is $0.19~\times~10^{-3}$. A study of intermediate states occurring in the $K^{-}K^{+}\pi^{-}\nu_{\tau}$ and $K^{-}\pi^{+}\pi^{-}\nu_{\tau}$ decays is also presented.