On the Analytic "Causal" Model for the QCD Running Coupling

Abstract

We discuss the model ${\bar{\alpha }}_{an}(Q^2)$ recently proposed for the QCD running coupling ${\bar{\alpha }}_s(Q^2)$ in the Euclidean domain on the basis of the "asymptotic-freedom" expression and on causality condition in the form of the $Q^2$-analyticity. The model contains no adjustable parameters and obeys the important features: (i) Finite ghost-free behavior in the "low $Q^2$" region and correspondence with the standard RG-summed UV expressions;%\item~ % (ii) The universal limiting value ${\bar{\alpha }}_{an}(0)$ expressed only via group symmetry factors. This value as well as the ${\bar{\alpha }}_{an}$ behavior in the whole IR region $Q^2\le {\Lambda }^2$ turns out to be stable with respect to higher loop corrections; %\item~ (iii) Coherence between observed ${\bar{\alpha }}_s(M_{\tau }^2)$ value and integral information on the IR ${\bar{\alpha }}_s(Q^2)$ behavior extracted from jet physics.

Comments: 4 pages, LaTex with psfig.sty, 2 PostScript figures