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.