Strange-Quark Mass from Tau-Lepton Decays withO(αs3)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 $O({\alpha }_s^3)$ accuracy. In agreement with previous estimates, the newly computed ${\alpha }_s^3$ term proves to be rather large. This justifies inclusion of the similarly estimated ${\alpha }_s^4$ term in phenomenological analysis. Combined with an updated value of $V_{\mathrm{us}}$ 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%.