Bjorken polarised sum rule with IR-finite QCD coupling

We evaluate the Bjorken polarised sum rule (BSR) ${\bar{\Gamma }}_1^{p-n}\left(Q^2\right)$ with truncated Operator Product Expansion (OPE) up to the dimension $D=4$ terms; the leading-twist ($D=0$) contribution is evaluated with a renormalon motivated resummation, where we use the IR-finite running coupling free of Landau singularities. The free residue parameters at the $D=2$ and $D=4$ terms are then extracted by fits to the experimental BSR data. In comparison to the case when perturbative QCD coupling is used in this approach (cf. Refs. [1], [2]), many advantages become manifest in the present case: (a) no regularisation in the resummation integral is needed; (b) the $Q^2$-interval in the fit can be significantly extended to lower $Q^2$-values; (c) the extracted residue parameter values are more stable, this being reflected in the significantly reduced experimental uncertainties of these values and the suppressed (almost negligible) central extracted value of the $D=4$ residue parameter (${\mu }_6$).