Large-order behaviour of the QCD Adler D-function in planar approximation

We consider the structure of the leading ultra-violet (UV) renormalon singularity associated with the QCD vacuum polarization Adler D-function, in the approximation that only planar Feynman diagrams are retained. This “planar approximation” results in some simplifications, in particular three of the four potential contributions from four-fermion operators are shown to be absent. We are able to obtain a fully normalized result for the leading n → ∞ behaviour of the portion of perturbative coefficients proportional to Nfn-r Nr, for SU(N) QCD with Nf quark flavours.