Estimates of higher-order contributions for perturbative series in QCD, in view of their asymptotic nature, are delicate, though indispensable for a reliable error assessment in phenomenological applications. In this work, the Adler function and the scalar correlator are investigated, and models for Borel transforms of their perturbative series are constructed, which respect general constraints 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, previous results obtained directly in the \(\overline{\mathrm{MS}}\) scheme are supported. Corresponding results for the scalar correlation function are new. It turns out that the substantially larger perturbative corrections for the scalar correlator in \(\overline{\mathrm{MS}}\) are dominantly due to this scheme choice, and can be largely reduced through more appropriate renormalisation schemes, which are easy to realise in the C-scheme.

鉴于其渐近性质，对 QCD 中微扰序列的高阶贡献的估计是微妙的，尽管对于现象学应用中的可靠误差评估是必不可少的。在这项工作中，研究了 Adler 函数和标量相关器，并构建了它们的微扰级数的 Borel 变换模型，该模型尊重算子乘积展开和重整化群的一般约束。作为一种新的成分，QCD耦合用于所谓的C - scheme，具有一定的优势。对于 Adler 函数，之前的结果直接在\(\overline{\mathrm{MS}}\)方案得到支持。标量相关函数的相应结果是新的。事实证明，\(\overline{\mathrm{MS}}\)中标量相关器的大得多的扰动校正主要是由于这种方案选择，并且可以通过更合适的重整化方案大大减少，这些方案很容易在C方案中实现。