Bjorken sum rule with hyperasymptotic precision

TL;DR

This paper enhances the precision of the Bjorken sum rule calculation by incorporating hyperasymptotic methods and renormalon analysis, achieving better agreement with experimental data.

Contribution

It introduces an improved determination of the infrared renormalon normalization and applies hyperasymptotic techniques to refine the sum rule calculation.

Findings

Good agreement with experimental data for $Q^2 extgreater= 1$ GeV$^2$

Estimated higher order perturbative terms

Refined renormalon normalization $Z_B(n_f=3)$

Abstract

We obtain an improved determination of the normalization of the leading infrared renormalon of the Bjorken sum rule: $Z_B (n_f=3)= -0.407\pm 0.119 $. Estimates of higher order terms of the perturbative series are given. We compute the Bjorken sum rule with hyperasymptotic precision by including the leading terminant, associated with the first infrared renormalon. We fit the experimental data to the operator product expansion theoretical prediction with $\hat f_{3}^{\rm PV}$ as the free parameter. We obtain a good agreement with the experiment with $\hat f_{3}^{\rm PV}\times 10^3=32^{+187}_{-196}\;{\rm GeV}^{2}$ for $Q^2 \geq 1$ GeV$^2$.