Optimizing the FESR extraction of m(s) from hadronic tau decay data

As is well known, the difference between zed and us vector and/or axial vec tor correlators, whose spectral functions are measurable in hadronic tau de cay, allows one in principle, through the use of QCD sum rules, to determin e the strange quark mass, ms. We show that, by studying the behavior of the relevant correlator difference in the complex q(2)-plane, the freedom to c hoose arbitrary analytic weight functions present in the finite energy sum rule (FESR) implementation of this approach may be exploited to construct F ESR's which (1) significantly reduce theoretical uncertainties and (2) remo ve problems associated with both the poor convergence of the OPE representa tion of the longitudinal part of the us vector and axial vector correlators and the large statistical errors in the us spectral data above the K* regi on. The result of this optimization is an extraction, based on present data , m(s) (2 GeV) = 115.1 +/- 13.6 +/- 11.8 +/- 9.7, where the first error is statistical, the second due to that on V-us, and the third theoretical. We show also that, for the new weights constructed here, analyses with errors in the us data in the K* region reduced by a factor of 2 would produce a de termination of m, with the statistical error reduced significantly below th at associated with the uncertainty in V-us.