$K^{0}_{S}$ production in $\tau$ decays

From a sample of about 160k $\mbox{Z}\!\!\to\!\!\tau^+\tau^-$ candidates collected with the ALEPH detector at LEP between 1991 and 1995, $\tau$ lepton decays involving $K^0_S\!\to\!\pi^+\pi^-$ are studied. The $K^0_SK^0_L$ associated production in $\tau$ decays is also investigated. The branching ratios are measured for the inclusive decay $B(\tau^-\!\!\to\!\!K^0_SX^-\nu_\tau)=(9.70\!\pm\!0.58\!\pm\!0.62)\ times10^{-3}$ , where $X^-$ can be anything, and for the exclusive decays \begin{center} \begin{tabular}{rcl} $B(\tau^-\!\!\to\!\!\overline{K}^0\pi^-\nu_\tau)$&=&$(8.55\!\pm\!1. 17\! \pm\!0.66)\times10^{-3}$,\\ $B(\tau^-\!\!\to\!\!\overline{K}^0\pi ^-\pi^0\nu_\tau)$&=&$(2.94\!\pm\! 0.73\!\pm\!0.37)\times10^{-3}$, \\ $B(\tau^-\!\!\to\!\!\overline{K} ^0K^-\nu_\tau)$&=&$(1.58\!\pm\!0.42\!\pm\! 0.17)\times10^{-3}$, \\ $B(\tau^-\!\!\to\!\!\overline{K}^0K^-\pi^0\nu_\tau)$&=&$(1.52\!\pm\ !0.76\! \pm\!0.21)\times10^{-3}$. \\ \end{tabular} \end{center} The decays $\tau^-\!\!\to\!\!K^0_SK^0_L\pi^-\nu_\tau$ is studied for the first time, giving a branching ratio \begin{center} \begin{tabular}{rcl} $B(\tau^-\!\!\to\!\!K^0_SK^0_L\pi^-\nu_\tau)$&=&$ (1.01\!\pm\!0.23\!\pm\!0.13)\times10^{-3}.$ \end{tabular} \end{center} The channels $\tau^-~\!\!\!\to\!\!\!~K^0_SK^0_S\pi^-\nu_\tau~$, $\tau^-~\!\!\!\to\!\!\!~K^0_SK^0_S\pi^-\pi^0\nu_\tau~$, $\tau^-~\!\!\!\to\!\!\!~K^0_SK^0_L\pi^-\pi^0\nu_\tau~$, $\tau^-~\!\!\!\to\!\!\!~\overline{K}^0\pi^-\pi^0\pi^0\nu_\tau$, $\tau^-~\!\!\!\to\!\!\!~K^0K^-\pi^0\pi^0\nu_\tau$ and $\tau^-~\!\!\!\to\!\!\!~K^0h^+h^-h^-\nu_\tau$ are also investigated. In addition, mass spectra in the $K^0_Sh^-$ and $K^0_Sh^-\pi^0$ final states are analysed to provide information on the intermediate states produced in the decays.