Conformal expansions and renormalons

The coefficients in perturbative expansions in gauge theories are factoriallyincreasing, predominantly due to renormalons. This type of factorial increaseis not expected in conformal theories. In QCD conformal relations betweenobservables can be defined in the presence of a perturbative infraredfixed-point. Using the Banks-Zaks expansion we study the effect of thelarge-order behavior of the perturbative series on the conformal coefficients.We find that in general these coefficients become factorially increasing.However, when the factorial behavior genuinely originates in a renormalonintegral, as implied by a postulated skeleton expansion, it does not affect theconformal coefficients. As a consequence, the conformal coefficients willindeed be free of renormalon divergence, in accordance with previousobservations concerning the smallness of these coefficients for specificobservables. We further show that the correspondence of the BLM method with theskeleton expansion implies a unique scale-setting procedure. The BLMcoefficients can be interpreted as the conformal coefficients in the seriesrelating the fixed-point value of the observable with that of the skeletoneffective charge. Through the skeleton expansion the relevance ofrenormalon-free conformal coefficients extends to real-world QCD.