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${}^2$.

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

References in corpus (9)

• Adler Function, Bjorken Sum Rule, and the Crewther Relation to Order alpha_s^4 in a General Gauge Theory
• Experimental study of isovector spin sum rules
• Analysis of nucleon electromagnetic form factors from light-front holographic QCD : The spacelike region
• High precision determination of the $Q^2$-evolution of the Bjorken Sum
• The bottom quark mass from the ${\rm Y}(1S)$ system at NNNLO
• Final COMPASS results on the deuteron spin-dependent structure function $g_1^{\mathrm{d}}$ and the Bjorken sum rule
• Proton Spin Structure in the Resonance Region
• Superasymptotic and hyperasymptotic approximation to the operator product expansion
• Adler Function, DIS sum rules and Crewther Relations