RG solutions for α_s at large N_c in d=3+1 QCD

Solutions of RG equations for $β(α)$ and $α(Q)$ are found in the class of meromorphic functions satisfying asymptotic conditions at large $Q$ (resp. small $α)$, and analyticity properties in the $Q^2$ plane. The resulting $α_R(Q)$ is finite in the Euclidean $Q^2$ region and agrees well at $Q\geq 1$ GeV with the $\bar{MS} α_s(Q)$.

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