The three-loop polarized pure singlet operator matrix element with two different masses

TL;DR

This paper computes the two-mass polarized pure singlet operator matrix element at three loops in QCD, providing essential ingredients for high-precision polarized structure function calculations involving heavy quarks.

Contribution

It presents the first three-loop two-mass polarized operator matrix element in x-space, including generalized iterated integrals with mass ratio dependence.

Findings

Provides explicit three-loop two-mass polarized operator matrix element

Includes generalized iterated integrals with square-root alphabet

Enables improved calculations of polarized structure functions at high precision

Abstract

We present the two-mass QCD contributions to the polarized pure singlet operator matrix element at three loop order in $x$-space. These terms are relevant for calculating the polarized structure function $g_1(x,Q^2)$ at $O(\alpha_s^3)$ as well as for the matching relations in the variable flavor number scheme and the polarized heavy quark distribution functions at the same order. The result for the operator matrix element is given in terms of generalized iterated integrals. These integrals depend on the mass ratio through the main argument, and the alphabet includes square--root valued letters.