${\alpha }_s(m_Z)$ from tau decays with matching conditions at three loops

Abstract

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 ${\alpha }_s(m_{t}au)$ 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 ${\alpha }_s(m_Z)$.

Comments: Latex, 11 pp., 3 figures. Uses elsart