Updated Determination of Ellis-Jaffe Sum Rules up to ${\mathrm{N}}^3\mathrm{LO}$ 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 (${\mathrm{N}}^3\mathrm{LO}$) 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 $\hat{I}{\pm }_s$ Landau pole near the asymptotic scale, we incorporate the low-energy $\hat{I}{\pm }_s$ 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 $\ddot{I}{‡}^2/d.o.f{|}_{Conv.}=1.86$ to $\ddot{I}{‡}^2/d.o.f{|}_{\mathrm{PMC}}=1.19$, thereby validating the effectiveness of our approach.

8 pages, 4 figures