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We discuss the prescription for the Dirac matrix gamma_5 in dimensionalregularization used in most second- and third-order QCD calculations ofcollider cross sections. We provide an alternative implementation of thisapproach 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 ineach fermion trace. This treatment is checked by computing the third-ordercorrections to the structure functions F_2 and g_1 in charged-currentdeep-inelastic scattering with axial-vector couplings to the W-bosons. Wederive the so far unknown third-order helicity-difference splitting functionDelta 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. Thisfunction is negligible at momentum fractions x >~ 0.3 but relevant at x << 1.

On gamma_5 in higher-order QCD calculations and the NNLO evolution of the polarized valence distribution