Strange quark mass from flavor breaking in hadronic $\tau$ decays

The strange quark mass is extracted from a finite energy sum rule (FESR) analysis of the flavor-breaking difference of light-light and light-strange quark vector-plus-axial-vector correlators, using spectral functions determined from hadronic $\tau$ decay data. We point out problems for existing FESR treatments associated with potentially slow convergence of the perturbative series for the mass-dependent terms in the OPE over certain parts of the FESR contour, and show how to construct alternate weight choices which not only cure this problem, but also (1) considerably improve the convergence of the integrated perturbative series, (2) strongly suppress contributions from the region of s values where the errors on the strange current spectral function are still large and (3) essentially completely remove uncertainties associated with the subtraction of longitudinal contributions to the experimental decay distributions. The result is an extraction of $m_s$ with statistical errors comparable to those associated with the current experimental uncertainties in the determination of the CKM angle, $V_{\mathrm{us}}.$ We find $m_s(1\mathrm{}$ $\mathrm{GeV})=158.6\mathrm{}\pm 18.7\pm 16.3\pm 13.3$ MeV (where the first error is statistical, the second due to that on $V_{\mathrm{us}},$ and the third theoretical).