The αs3 corrections to the Bjorken sum rule for polarized electroproduction and to the Gross-Llewellyn Smith sum rule

We have computed the next-next-to-leading order QCD corrections to the Gross-Llewellyn Smith sum rule for deep inelastic neutrino-nucleon scattering and to the Bjorken sum rule for polarized electron-nucleon scattering. This involved the proper treatment of γ5 inside the loop integrals within dimensional regularization. We find that the difference between the two sum rules are entirely due to a class of six three-loop graphs and is of the order of 1% of the leading QCD term (O(αs)). Hence the Q2 behavior of both sum rules should be nearly the same if the physics is described adequately by the lower order terms of perturbative QCD. (orig.)