Analytic QCD running coupling with finite IR behaviour and universal   ${\bar \alpha}_s(0)$ value
  As is known from QED, a possible solution to the ghost-pole trouble can be obtained by imposing the $Q^2$-analyticity imperative. Here, the pole is compensated by the $\alpha$ non-analytic contribution that results in finite coupling renormalization.   We apply this idea to QCD and arrive at the $Q^2$ analytic $\bar{\alpha}_s(Q)$. This solution corresponds to perturbation expansion, obeys AF and, due to non-perturbative contribution, has a regular IR behaviour. It does not contain any adjustable parameter and has a finite IR limit $\bar{\alpha}_s(0)$ which depends only on group symmetry factors. In the one-loop approximation it is equal to $4\pi/\beta_0 \simeq 1.40\,$ and turns out to be surprisingly stable with respect to higher order corrections. On the other hand, the IR behaviour of our new analytic solution agrees with recent global low energy experimental estimates of $\bar{\alpha}_s(Q^2)$. 
D.V. Shirkov and I.L. Solovtsov