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

Abstract.

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 $K\overline{K}\pi$ 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 $m_s(1 {\rm GeV}^2) = (234^{\,+61}_{\,-76}){\rm MeV}/c^2$.