Analytic invariant charge: non-perturbative aspects
  A brief review of the recently developed model for the QCD analytic invariant charge is presented. The main idea of this approach is invoking the analyticity condition into the framework of the renormalization group method. More precisely, the analyticity requirement is explicitly imposed on the perturbative expansion of the $\beta$ function for restoring its correct analytic properties. The model possesses a number of profitable features. Namely, the analytic invariant charge has no unphysical peculiarities at any loop level; it contains no free parameters; it incorporates ultraviolet asymptotic freedom with infrared enhancement; it has universal behavior both in ultraviolet and infrared regions at any loop level; it possesses a good higher loop and scheme stability. There is considerable difference between the respective values of analytic invariant charge in the low-energy domain of spacelike and timelike regions. The approach proposed enables one to describe various strong interaction processes both of perturbative and intrinsically non-perturbative nature. 
A.V. Nesterenko