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.

doi:10.1016/j.physletb.2015.07.027

Report/Journal Article

PUBDB-2017-05452

On ${\gamma }_{5}$ in higher-order QCD calculations and the NNLO evolution of the polarized valence distribution

Moch, S.Extern* ; Vermaseren, J. A. M. ; Vogt, A. (Corresponding author)

2015
Elsevier Amsterdam

Physics letters / B 748, 432 - 438 (2015) [10.1016/j.physletb.2015.07.027]

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Please use a persistent id in citations: doi:10.1016/j.physletb.2015.07.027 doi:10.3204/PUBDB-2017-05452

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 $x \gtrsim$ 0.3 but relevant at $x \ll$ 1.

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