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 τ lepton. The decays τ-→ (Kπ) -ντ, (Kππ)-ντ and (Kπππ) - 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 η mesons. The reconstructed strange final states, corrected for resolution effects and detection efficiencies, yield the strange spectral function of the τ 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(τ - → K-π0ντ) = (0.471 ±0.059stat±0.023sys) % and B(τ -→ K-π+π-ντ) = (0.415 ± 0.053stat ± 0.040sys) % have been measured.
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