Study of τ\tau decays involving kaons, spectral functions and determination of the strange quark mass

All ALEPH measurements of branching ratios of tau decays involving kaons are summarized including a combination of results obtained with K^0_S and K^0_L detection. The decay dynamics are studied, leading to the determination of contributions from vector K^*(892) and K^{*}(1410), and axial-vector K_1(1270) and K_1(1400) resonances. Agreement with isospin symmetry is observed among the different final states. Under the hypothesis of the conserved vector current, the spectral function for the K\bar{K}\pi mode is compared with the corresponding cross section for low energy e^+e^- annihilation, yielding an axial-vector fraction of (94^{+6}_{-8})% for this mode. The branching ratio for tau decay into all strange final states is determined to be B(\tau^-\to X^-(S=-1)\nu_\tau)=(28.7\pm1.2)\times 10^{-3}. The measured mass spectra of the strange tau decay modes are exploited to derive the S=-1 spectral function. A combination of strange and nonstrange spectral functions is used to determine the strange quark mass and nonperturbative contributions to the strange hadronic width. A method is developed to avoid the bad convergence of the spin zero hadronic component, with the result m_s(M_\tau^2)=(176^{\,+46}_{\, -57}) MeV/c^2. The evolution down to 1~GeV gives m_s(1~{\rm GeV}^2) = (234^{\,+61}_{\,-76})~{\rm MeV}/c^2

One-prong τ\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} $B(\tau^-\to K^-\nu_\tau)$ &=& $(6.96\pm0.25\pm0.14)\times 10^{-3}$,\\ $B(\tau^-\to K^-\pi^0\nu_\tau)$ &=& $(4.44\pm0.26\pm0.24)\times 10^{-3}$,\\ $B(\tau^-\to K^-\pi^0\pi^0\nu_\tau)$ &=& $(0.56\pm0.20\pm0.15)\times 10^{-3}$,\\ $B(\tau^-\to K^-\pi^0\pi^0\pi^0\nu_\tau)$ &=& $(0.37\pm0.21\pm0.11)\times 10^{-3}$,\\ $B(\tau^-\to K^-K^{0}\nu_\tau)$ &=& $(1.62\pm0.21\pm0.11)\ times 10^{-3}$,\\ $B(\tau^-\to K^{-}K^{0}\pi^0\nu_\tau)$