2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/190540Using the recent four-loop calculations of the QCD beta-function and the three-loop matching coefficients we study the induced error in $α_s(m_Z)$ obtained from $α_s(m_tau)$ 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 $α_s(m_Z)$.Latex, 11 pp., 3 figures. Uses elsartHigh Energy Physics - Phenomenology$α_s(m_Z)$ from tau decays with matching conditions at three loopstext