Measurement of the strange spectral function in hadronic $\tau$ decays

Abstract.

Tau lepton decays with open strangeness in the final state are measured with the OPAL detector at LEP to determine the strange hadronic spectral function of the $\tau$ lepton. The decays $\tau^{-}\rightarrow(K\pi)^{-}\nu_{\tau}$, $(\pi\pi)^{-}\nu_{\tau}$ and $(K\pi\pi\pi)^{-}\nu_{\tau}$ with final states consisting of neutral and charged kaons and pions have been studied. The invariant mass distributions of $93.4\%$ of these final states have been experimentally determined. Monte Carlo simulations have been used for the remaining $6.6\%$ and for the strange final states including $\eta$ mesons. The reconstructed strange final states, corrected for resolution effects and detection efficiencies, yield the strange spectral function of the $\tau$ lepton. The moments of the spectral function and the ratio of strange to non-strange moments, which are important input parameters for theoretical analyses, are determined. Furthermore, the branching fractions $B(\tau^{-}\rightarrow K^{-}\pi^{0}\nu_{\tau}) = (0.471\pm0.059_{\mathrm{stat}}\pm0.023_{\mathrm{sys}})\%$ and $B(\tau^{-}\rightarrow K^{-}\pi^{ + }\pi^{-}\nu_{\tau}) = (0.415\pm0.053_{\mathrm{stat}}\pm0.040_{\mathrm{sys}})\%$ have been measured.