In this article we review the results of our recent work on the difference between the Borel representations of \(\tau \) hadronic spectral function moments obtained with the CIPT and FOPT methods. For the presentation of the theoretical results we focus on the large-\(\beta _0\) approximation, where all expressions can be written down in closed form, and we comment on the generalization to full QCD. The results may explain the discrepancy in the behavior of the FOPT and CIPT series that has been the topic of intense discussions in previous literature and which represents a major part of the theoretical uncertainties in current strong coupling determinations from hadronic \(\tau \) decays. The findings also imply that the OPE corrections for FOPT and CIPT differ and that the OPE corrections for CIPT do not have standard form.

在本文中，我们回顾了我们最近关于使用 CIPT 和 FOPT 方法获得的\(\tau \)强子谱函数矩的 Borel 表示之间的差异的工作结果。对于理论结果的介绍，我们关注大的\(\beta _0\)近似，其中所有表达式都可以写成封闭的形式，我们评论对全 QCD 的推广。结果可能解释了 FOPT 和 CIPT 系列行为的差异，这一直是以前文献中激烈讨论的主题，并且代表了当前强耦合确定的理论不确定性的主要部分强子\(\tau \)衰变。研究结果还暗示 FOPT 和 CIPT 的 OPE 修正不同，并且 CIPT 的 OPE 修正没有标准形式。