The perturbative quark mass corrections to the tau hadronic width are studied to O(αs m 2 q). Including up to dimension four corrections, we get ms(4GeV ) = (143 ± 42) MeV [ms(1GeV ) = (193 ± 59) MeV ]. Possible improvements to reduce the theoretical uncertainty are pointed out. September 1998 Invited talk at “High Energy Conference on Quantum Chromodynamics (QCD ’98)”, 2-8 July 1998, Montpellier. Work supported in part by CICYT and DGESIC, Spain (Grants No. AEN-96/1672 and PB97-1261), and by the European Union TMR Network EURODAPHNE (Contract No. ERBFMX-CT98-0169).
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