Strange-quark mass from tau-lepton decays with O(alpha3s) accuracy

The first complete calculation of the quadratic quark mass correction to the correlator of the two currents relevant for the strangeness-changing semihadronic tau-decay rate is presented including its real part at the four-loop level. This allows us to perform the extraction of the strange-quark mass m(s) from the decay width of the tau-lepton with full O(alpha3s) accuracy. In agreement with previous estimates, the newly computed alpha3s term proves to be rather large. This justifies inclusion of the similarly estimated alpha4s term in phenomenological analysis. Combined with an updated value of V us and an "improved" version of the renormalization group improvement of the perturbative series, this leads to an increase of the central value of m(s) by about 20% and a partial reduction of the theoretical uncertainty by about 50%.