Strong Coupling Constant with Flavour Thresholds at Four Loops in the MS-bar Scheme

Abstract

We present in analytic form the matching conditions for the strong coupling constant alpha_s^(n_f)(mu) at the flavour 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^(n_f)(mu) together with appropriate relationships between the asymptotic scale parameters Lambda^(n_f) for different numbers of flavours n_f.

10 pages (Latex), 3 figures (Postscript)

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• Estimations of Order alpha_s^3 and alpha_s^4 Corrections to Mass-Dependent Observables
• Perturbative relations between $e^{+}{e}^{-}$ annihilation and $\tau$ decay observables including resummation effects

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