Isospin Breaking and the Extraction of $m_s$ from the $τ$-Decay-Like Vector Current Sum Rule

Abstract

Narison's $τ$-decay-like sum rule for determining the strange quark mass is re-investigated, taking into account isospin-breaking corrections in the extraction of the input spectral functions from $e^+e^-\to hadrons$ data. The corrections, estimated using experimental data on vector meson electromagnetic decay constants and a QCD sum rule analysis of the 38 vector current correlator, are shown to be especially large for the isoscalar case. The reason such large corrections are natural is also explained. Due to the high degree of cancellation in the original sum rule, the effect of these corrections on the determination of $m_s$ is significant. A new central value $m_s=113-138 MeV$ is found, in the $\bar{MS}$ scheme at 1 GeV$^2$, with significant (asymmetric) errors associated with errors in the input experimental data.