Determination of the strange quark mass from Cabibbo-suppressed tau decays with resummed perturbation theory in an effective scheme

We present an analysis of the -corrections to Cabibbo-suppressed -lepton decays employing contour improved resummation within an effective scheme which is an essential new feature as compared to previous analyses. The whole perturbative QCD dynamics of the -system is described by the -function of the effective coupling constant and by two -functions for the effective mass parameters of the strange quark in different spin channels. We analyze the stability of our results with regard to high-order terms in the perturbative expansion of the renormalization group functions. A numerical value for the strange quark mass in the scheme is extracted: $m_s(M_\tau)=130\pm 27_{\mathrm{{exp}}}\pm 9_{\mathrm{{th}}}{\mathrm{ MeV}}$. After running to the scale this translates into . Received: 1 October 2000 / Revised version: 22 February 2001 / Published online: 18 May 2001