We discuss the prescription for the Dirac matrix gamma(5) in dimensional regularization used in most second- and third-order QCD calculations of collider cross sections. We provide an alternative implementation of this approach that avoids the use of an explicit form of gamma(5) and of its (anti-) commutation relations in the most important case of no more than one gamma(5) in each fermion trace. This treatment is checked by computing the third-order corrections to the structure functions F-2 and g(1) in charged-current deep-inelastic scattering with axial-vector couplings to the W-bosons. We derive the so far unknown third-order helicity-difference splitting function Delta P-ns((2)s) that contributes to the next-to-next-to-leading order (NNLO) evolution of the polarized valence quark distribution of the nucleon. This function is negligible at momentum fractions x greater than or similar to 0.3 but relevant at x << 1. (C) 2015 The Authors. Published by Elsevier B.V.
We discuss the prescription for the Dirac matrix γ5 in dimensional regularization used in most second- and third-order QCD calculations of collider cross sections. We provide an alternative implementation of this approach that avoids the use of an explicit form of γ5 and of its (anti-)commutation relations in the most important case of no more than one γ5 in each fermion trace. This treatment is checked by computing the third-order corrections to the structure functions F2 and g1 in charged-current deep-inelastic scattering with axial-vector couplings to the W-bosons. We derive the so far unknown third-order helicity-difference splitting function δPns(2)s that contributes to the next-to-next-to-leading order (NNLO) evolution of the polarized valence quark distribution of the nucleon. This function is negligible at momentum fractions x≳0.3 but relevant at x≪1.