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 αₛ^(nf)(μ) at the flavor thresholds to three loops in the modified minimal-subtraction scheme. Taking into account the recently calculated coefficient β₃ of the Callan-Symanzik beta function of quantum chromodynamics, we thus derive a four-loop formula for αₛ^(nf)(μ) together with appropriate relationships between the asymptotic scale parameters Λ^(nf) for different numbers of flavors nf.