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

• Received 17 August 2022
• Accepted 7 September 2022
• Corrected 10 October 2022

DOI:https://doi.org/10.1103/PhysRevD.106.056023

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Published by the American Physical Society