Infrared renormalons and the relations between the Gross–Llewellyn Smith and the Bjorken polarized and unpolarized sum rules

It is demonstrated that the infrared renormalon calculus indicates that the QCD theoretical expressions for the Gross–Llewellyn Smith sum rule and for the Bjorken polarized and unpolarized ones contain an identical negative twist-4 $1/Q^2$ correction. This observation is supported by the consideration of the results of calculations of the corresponding twist-4 matrix elements. Together with the indication of the similarity of perturbative QCD contributions to these three sum rules, this observation leads to simple new theoretical relations between the Gross–Llewellyn Smith and Bjorken polarized and unpolarized sum rules in the energy region $Q^2\geq 1\,{\rm GeV}^2$. The validity of this relation is checked using concrete experimental data for the Gross–Llewellyn Smith and Bjorken polarized sum rules.