Bjorken sum rule with hyperasymptotic precision

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 ${\hat{f}}_3^{\mathrm{PV}}$ as the free parameter. We obtain a good agreement with the experiment with ${\hat{f}}_3^{\mathrm{PV}}\times 10^3=32_{-196}^{+187}{\mathrm{GeV}}^2$ for $Q^2\ge 1$ GeV${}^2$.

Comments: 25 pages, 8 Figures; v2: small numerical modification due to finite charm mass corrections. Physical results unchanged. References added. It matches the PRD version