Strong-Coupling Constant with Flavor Thresholds at Five Loops in the Modified Minimal-Subtraction Scheme
Bernd A. Kniehl, Anatoly Vassilievich Kotikov, Андрей Иванович Онищенко, Oleg L. Veretin · Physical Review Letters · 2006
We present in analytic form the matching conditions for the strong-coupling constant ${\ensuremath{\alpha}}_{s}^{({n}_{f})}(\ensuremath{\mu})$ at the flavor thresholds to four loops in the modified minimal-subtraction scheme. Taking into account the present knowledge on the coefficient ${\ensuremath{\beta}}_{4}$ of the Callan-Symanzik beta function of quantum chromodynamics, we thus derive a five-loop formula for ${\ensuremath{\alpha}}_{s}^{({n}_{f})}(\ensuremath{\mu})$ together with appropriate relationships between the asymptotic scale parameters ${\ensuremath{\Lambda}}^{({n}_{f})}$ for different numbers of flavors ${n}_{f}$.