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