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We present in analytic form the matching conditions for the strong coupling constant ₒ^ ({n₅) } () at the flavor thresholds to three loops in the modified minimal-subtraction scheme. Taking into account the recently calculated coefficient ₃ of the Callan-Symanzik beta function of quantum chromodynamics, we thus derive a four-loop formula for ₒ^ ({n₅) } () together with appropriate relationships between the asymptotic scale parameters ^ ({n₅) } for different numbers of flavors n₅.
Chetyrkin et al. (Mon,) studied this question.
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