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

Moch, S.; Vogt, A.; Vermaseren, J. A. M.

Report/Internal Report

PUBDB-2015-02312

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

Moch, S. ; Vermaseren, J. A. M. ; Vogt, A.

2015

11 p. (2015)

This record in other databases:

Report No.: DESY-15-061; LTH-1042; NIKHEF-15-018; arXiv:1506.04517

Abstract: 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 >~ 0.3 but relevant at x << 1.

Keyword(s): regularization: dimensional ; coupling: axial-vector ; higher-order: 2 ; quark: valence ; quantum chromodynamics ; deep inelastic scattering ; commutation relations ; structure function ; splitting function ; charged current ; nucleon