STRONG-COUPLING CONSTANT WITH FLAVOR THRESHOLDS AT 4 LOOPS IN THE MODIFIED MINIMAL-SUBTRACTION SCHEME

We present in analytic form the matching conditions for the strong cou pling constant alpha(s)((nf))(mu) at the flavor thresholds to three lo ops in the modified minimal-subtraction scheme. Taking into account th e 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 betwee n the asymptotic scale parameters Lambda((nf)) for different numbers o f flavors n(f).