On the analytically-improved running coupling in QCD

In this paper, we examine, in the 't Hooft renormalization scheme, the analytic running coupling (alpha) over bar (t)(Q(2)) in QCD, using the two-loop beta-function with positive expansion parameters beta(0) and beta(1). An exact integral representation is derived for this causal coupling, which is fully expressed in terms of the imaginary part of the Lambert function W. This integral form manifestly accounts for the universal value of the infrared limit (alpha) over bar (t)(Q(2) = 0) = 4 pi/beta(0).

Automated summary

In this paper, we investigate the behavior of the analytic running coupling in QCD using the 't Hooft renormalization scheme and the two-loop beta-function. We derive an exact integral representation for this causal coupling, which is expressed in terms of the Lambert function W's imaginary part. This integral form manifestly accounts for the universal value of the infrared limit.