====== TTP97-26 $\alpha_s(m_Z)$ from tau decays with matching conditions at three loops ====== Using the recent four-loop calculations of the QCD beta-function and the three-loop matching coefficients we study the induced error in $\alpha_s(m_Z)$ obtained from $\alpha_s(m_tau)$ due to the evolution procedure. We show that, when consistent matching and running is used at this order, these errors are pushed below 0.0005 in $\alpha_s(m_Z)$. |**German Rodrigo (Karlsruhe U.), Antonio Pich, Arcadi Santamaria (Valencia U.)** | |** Phys. Lett. B 424 367-374 1998 ** | | {{preprints:1997:ttp97-26.pdf|PDF}} {{preprints:1997:ttp97-26.ps|PostScript}} [[http://arxiv.org/abs/hep-ph/9707474|arXiv]] | | |