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

Abstract

We calculate the massive polarized three-loop pure singlet operator matrix element $A_{Qq}^{(3),\mathrm{PS}}$ in the single mass case in the Larin scheme. This operator matrix element contributes to the massive polarized three-loop Wilson coefficient $H_{Qq}^{(3),\mathrm{PS}}$ 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 $x$.

25 pages Latex, 2 Figures