Generalized Crewther relation and a novel demonstration of the scheme independence of commensurate scale relations up to all orders * *Supported by the Chongqing Graduate Research and Innovation Foundation (ydstd1912, CYB21045), the National Natural Science Foundation of China (11625520, 12047564) and the Fundamental Research Funds for the Central Universities (2020CQJQY-Z003)

Abstract

In this study, we investigate in detail the generalized Crewther Relation (GCR) between the Adler function (D) and the Gross-Llewellyn Smith sum rules coefficient ( ) using the newly proposed single-scale approach of the principle of maximum conformality (PMC). The resultant GCR is scheme-independent, with the residual scale dependence due to unknown higher-order terms highly suppressed. Thus, a precise test of QCD theory without renormalization schemes and scale ambiguities can be achieved by comparing with data. Moreover, a demonstration of the scheme independence of the commensurate scale relation up to all orders is presented. Additionally, for the first time, the Pade approximation approach has been adopted for estimating the unknown -loop contributions from the known four-loop perturbative series.