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Estimates of higher-order contributions for perturbative series in QCD, inview of their asymptotic nature, are delicate, though indispensable for areliable error assessment in phenomenological applications. In this work, theAdler function and the scalar correlator are investigated, and models for Boreltransforms of their perturbative series are constructed, which respect generalconstraints from the operator product expansion and the renormalisation group.As a novel ingredient, the QCD coupling is employed in the so-called$C$-scheme, which has certain advantages. For the Adler function, previousresults obtained directly in the $\overline{\rm MS}$ scheme are supported.Corresponding results for the scalar correlation function are new. It turns outthat the substantially larger perturbative corrections for the scalarcorrelator in $\overline{\rm MS}$ are dominantly due to this scheme choice, andcan be largely reduced through more appropriate renormalisation schemes, whichare easy to realise in the $C$-scheme.

Higher-order behaviour of two-point current correlators