The singlet contribution to the Bjorken sum rule for polarized deep inelastic scattering

It is shown that the existing four-loop result for the Bjorken polarized sum rule for deep inelastic electron-nucleon scattering obtained within perturbative Quantum Chromodynamics should be supplemented by the calculation of the diagrams of the so-called singlet type. We also give an explanation of the interesting coincidence of two different classes of diagrams, one of the non-singlet and one of the singlet type, contributing the alpha(4)(s)-approximation to the total cross-section of electron-positron annihilation into hadrons. (C) 2013 Elsevier B.V. All rights reserved.