The Gross--Llewellyn Smith Sum Rule in the Analytic Approach to Perturbative QCD

We apply analytic perturbation theory to the Gross--Llewellyn Smith sum rule. We study the $Q^2$ evolution and the renormalization scheme dependence of the analytic three-loop QCD correction to this sum rule, and demonstrate that the results are practically renormalization scheme independent and lead to rather different $Q^2$ evolution than the standard perturbative correction possesses.