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

TL;DR

This paper refines the theoretical prediction of the Ellis-Jaffe Sum Rule by applying the Principle of Maximum Conformality up to N³LO and incorporating an analytic perturbation theory model to improve agreement with experimental data.

Contribution

It introduces a combined approach using PMC and APT to enhance the precision of EJSR predictions at high perturbative orders, reducing theoretical uncertainties.

Findings

Improved agreement between theory and experiment for EJSR.

Reduced chi-squared discrepancy from 1.86 to 1.19.

Validated the effectiveness of PMC and APT in QCD calculations.

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.