Measurement of the Strangeness Spectral Function and the Mass of the Strange Quark in Hadronic tau Decays with the OPAL Detector

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 and the mass of the strange quark. The decays τ −→ (Kπ) −ντ , (Kππ) −ντ and (Kπππ) −ντ with final states consisting of neutral and charged kaons and pions, have been studied. The invariant mass distribution 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 −π 0 ντ ) = (0.471 ± 0.064stat ± 0.021sys) % B(τ − → K −π +π −ντ ) = (0.415 ± 0.059stat ± 0.031sys) % have been measured. From the CKM weighted difference of strange and non-strange spectral moments, the mass of the strange quark at the τ mass scale has been determined ms(m2 τ ) = (84 ± 14exp ± 6Vus ± 17theo) MeV. Evolving this result to customary scales yields ms(1 GeV2 ) = (111+26 −35) MeV ms(4 GeV2 ) = (82+19 −25) MeV.