Disentangling running coupling and conformal effects in QCD
  We investigate the relation between a postulated skeleton expansion and the conformal limit of QCD. We begin by developing some consequences of an Abelian-like skeleton expansion, which allows one to disentangle running-coupling effects from the remaining skeleton coefficients. The latter are by construction renormalon-free, and hence hopefully better behaved. We consider a simple ansatz for the expansion, where an observable is written as a sum of integrals over the running-coupling. We show that in this framework one can set a unique Brodsky-Lepage-Mackenzie (BLM) scale-setting procedure as an approximation to the running-coupling integrals, where the BLM coefficients coincide with the skeleton ones. Alternatively, the running-coupling integrals can be approximated using the effective charge method. We discuss the limitations in disentangling running coupling effects in the absence of a diagrammatic construction of the skeleton expansion. Independently of the assumed skeleton structure we show that BLM coefficients coincide with the conformal coefficients defined in the small $\beta_0$ (Banks-Zaks) limit where a perturbative infrared fixed-point is present. This interpretation of the BLM coefficients should explain their previously observed simplicity and smallness. Numerical examples are critically discussed. 
Stanley J. Brodsky, Einan Gardi, Georges Grunberg and Johan Rathsman