Bjorken sum rule with hyperasymptotic precision

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 +/- 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 (f) over cap (PV)(3) as the free parameter. We obtain a good agreement with the experiment with (f) over cap (PV)(3) x 10(3) = 32(-196)(+187) GeV2 for Q(2) >= 1 GeV2.

Automated summary

In this study, we obtain an improved determination of the normalization of the leading infrared renormalon in the Bjorken sum rule and provide estimates of higher order terms. By including the leading terminant associated with the first infrared renormalon, we compute the Bjorken sum rule with hyperasymptotic precision. The experimental data is fitted to the theoretical prediction and shows good agreement.