Renormalon structure in Bjorken sum rule

Abstract

Leading-twist Bjorken polarised sum rule (BSR) ${\bar{\Gamma }}_1^{p-n}\left(Q^2\right)$ is evaluated using its known renormalon structure. In addition, we add OPE terms with the dimension $D=2,4$, and fit this to experimental data for inelastic BSR in specific intervals of momenta, $Q^2\ge Q_{\min }^2$, where $Q_{\min }^2\approx (1.7\pm 0.3){\mathrm{GeV}}^2$. Reasonable values of the pQCD coupling can be extracted only for specific choices of $Q_{\min }^2$, but have in general, for other choices of $Q_{\min }^2$, very large uncertainties and thus cannot be extracted in practice. On the other hand, if we fix the pQCD coupling to the known world average values, the $D=2$ and $D=4$ OPE terms can be determined within reasonable uncertainties dominated by the experimental uncertainties of the data.