The Polarized Two-Loop Massive Pure Singlet Wilson Coefficient for Deep-Inelastic Scattering

J. Blümlein; C. G. Raab; K. Schönwald

doi:10.1016/j.nuclphysb.2019.114736

paper

The Polarized Two-Loop Massive Pure Singlet Wilson Coefficient for Deep-Inelastic Scattering

arXiv:1904.08911 · doi:10.1016/j.nuclphysb.2019.114736

Abstract

We calculate the polarized massive two--loop pure singlet Wilson coefficient contributing to the structure functions $g_{1} (x, Q^{2})$ analytically in the whole kinematic region. The Wilson coefficient contains Kummer--elliptic integrals. We derive the representation in the asymptotic region $Q^{2} ≫ m^{2}$ , retaining power corrections, and in the threshold region. The massless Wilson coefficient is recalculated. The corresponding twist--2 corrections to the structure function $g_{2} (x, Q^{2})$ are obtained by the Wandzura--Wilczek relation. Numerical results are presented.

22 pages Latex, 8 Figures