Optimizing the FESR extraction of ms from hadronic τ decay data

Abstract

As is well known, the difference between ud and us vector and/or axial vector correlators, whose spectral functions are measurable in hadronic τ decay, allows one in principle, through the use of QCD sum rules, to determine the strange quark mass, m s . We show that, by studying the behavior of the relevant correlator difference in the complex q 2-plane, the freedom to choose arbitrary analytic weight functions present in the finite energy sum rule (FESR) implementation of this approach may be exploited to construct FESR's which (1) significantly reduce theoretical uncertainties and (2) remove problems associated with both the poor convergence of the OPE representation 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* region. 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 determination of m s with the statistical error reduced significantly below that associated with the uncertainty in V us .