Updated Determination of Ellis-Jaffe Sum Rules up to $\rm N^{3}LO$ QCD corrections

Abstract

In this paper, we explore the properties of the Ellis-Jaffe Sum Rule (EJSR) by employing the Principle of Maximum Conformality (PMC) approach to address its perturbative part up to next-to-next-to-next-to-leading order ($\rm N^{3}LO$) QCD contributions. By applying the PMC, we achieve a precise perturbative QCD prediction for the EJSR, free from conventional ambiguities associated with the renormalization scale choices. Considering the presence of the $\alpha_s$ Landau pole near the asymptotic scale, we incorporate the low-energy $\alpha_s$ model based on analytic perturbation theory (APT) to refine the EJSR behavior in the infrared region. By combining the PMC approach with the low-energy APT model, the agreement between theoretical calculations and experimental measurements of EJSR is significantly improved, as evidenced by the reduced discrepancy from $\chi^{2}/d.o. f|_{\rm Conv.}=1.86$ to $\chi^{2}/d.o. f|_{\rm PMC}=1.19$, thereby validating the effectiveness of our approach.