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

## TL;DR

This paper analytically computes the polarized massive two-loop pure singlet Wilson coefficient for deep-inelastic scattering across all kinematic regions, including asymptotic and threshold limits, with numerical results provided.

## Contribution

It introduces an analytical calculation of the polarized massive two-loop pure singlet Wilson coefficient, including Kummer-elliptic integrals, and derives asymptotic and threshold representations.

## Key findings

- Analytical expression for the Wilson coefficient across all kinematic regions.
- Representation in the asymptotic region with power corrections.
- Numerical results illustrating the behavior of the Wilson coefficient.

## 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 $Q^2 \gg m^2$, 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.