Two-Loop Massive Operator Matrix Elements for Polarized and Unpolarized Deep-Inelastic Scattering

TL;DR

This paper addresses the need for precise heavy-flavor corrections in deep-inelastic scattering (DIS) at large $Q^2$ by computing the massive operator matrix elements (OMEs) at $O(\alpha_s^2)$ in Mellin space. The authors avoid integration-by-parts, instead using Mellin-Barnes and hypergeometric representations to obtain compact analytic forms in terms of nested harmonic sums, and they reduce the functional basis to two primary sums. They provide explicit expressions for the unpolarized and polarized gluon-to-quark OMEs, and they verify consistency with prior results BU1/BU2 while clarifying the structure of the harmonic-sum basis. The results enable efficient calculation of heavy-flavor Wilson coefficients for $F_2$, $g_1$ and $F_L$ in the asymptotic region, contributing to precision determinations of PDFs and $\Lambda_{\mathrm{QCD}}$.

Abstract

The $O(α_s^2)$ massive operator matrix elements for unpolarized and polarized heavy flavor production at asymptotic values $Q^2 >> m^2$ are calculated in Mellin space without applying the integration-by-parts method. We confirm previous results given in Refs. \cite{BU1,BU2}, however, obtain much more compact representations.