Investigation of a new analytic running coupling in QCD

The mathematical properties of the new analytic running coupling (NARC) in QCD are investigated. This running coupling naturally arises under analytization of the renormalization group equation. One of the crucial points in our consideration is the relation established between the NARC and its inverse function. The latter is expressed in terms of the so-called Lambert W function. This relation enables one to present explicitly the NARC in the renorminvariant form and to derive the corresponding beta function. The asymptotic behavior of this beta function is examined. The consistent estimation of the parameter Lambda (QCD) is given.