Study of $\tau$ 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