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

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.

21 pages LATEX, 3 Figures. arXiv admin note: substantial text overlap with arXiv:1711.06717

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Cited by in corpus (2)

• Parton Distributions in Nucleons and Nuclei
• The three-loop single mass polarized pure singlet operator matrix element