The three-loop single mass polarized pure singlet operator matrix element

TL;DR

This paper presents a detailed three-loop calculation of a polarized pure singlet operator matrix element in quantum chromodynamics, providing analytic results relevant for deep-inelastic scattering at high precision.

Contribution

It provides the first complete three-loop polarized pure singlet operator matrix element calculation in the single mass case, with analytic results in Mellin N and x space.

Findings

Analytic expressions for the operator matrix element in Mellin N and x space.

Behavior analysis of the matrix element at small and large x.

Contribution to the precision of polarized deep-inelastic scattering calculations.

Abstract

We calculate the massive polarized three-loop pure singlet operator matrix element $A_{Qq}^{(3), \rm PS}$ in the single mass case in the Larin scheme. This operator matrix element contributes to the massive polarized three-loop Wilson coefficient $H_{Qq}^{(3),\rm PS}$ in deep-inelastic scattering and constitutes a three-loop transition matrix element in the variable flavor number scheme. We provide analytic results in Mellin $N$ and in $x$ space and study the behaviour of this operator matrix element in the region of small and large values of the Bjorken variable $x$.