Strong coupling constant with flavor thresholds at four loops in the modified minimal-subtraction scheme

We present in analytic form the matching conditions for the strong coupling constant alpha(s)((nf))(mu) at the flavor thresholds to three loops in the modified minimal-subtraction scheme. Taking into account the recently calculated coefficient beta(3) Of the Callan-Symanzik beta function of quantum chromodynamics, we thus derive a four-loop formula for alpha(s)((nf))(mu) together with appropriate relationships between the asymptotic scale parameters Lambda((nf)) for different numbers of flavors n(f).