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

Abstract

Solutions of RG equations for $\beta (\alpha )$ and $\alpha (Q)$ are found in the class of meromorphic functions satisfying asymptotic conditions at large $Q$ (resp. small $\alpha )$, and analyticity properties in the $Q^2$ plane. The resulting ${\alpha }_R(Q)$ is finite in the Euclidean $Q^2$ region and agrees well at $Q\ge 1$ GeV with the $\overline{MS}{\alpha }_s(Q)$.

Comments: 11 pages, no figures, dedicated to the 70th birthday of Professor Francesco Calogero, subm. to the Journal of Nonlinear Mathematical Physics