Moments of the 3--loop corrections to the heavy flavor contribution to $F_2(x,Q^2)$ for $Q^2\gg m^2$

TL;DR

This paper computes three-loop heavy flavor corrections to the structure function F_2(x,Q^2) at high Q^2, providing precise moments of Wilson coefficients and operator matrix elements crucial for QCD analyses.

Contribution

It presents the first independent calculation of moments of fermionic contributions to three-loop anomalous dimensions of twist-2 operators in unpolarized deep inelastic scattering.

Findings

Calculated moments of heavy flavor Wilson coefficients at three loops.

Recalculated moments of fermionic contributions to anomalous dimensions.

Enhanced precision in QCD predictions for structure functions.

Abstract

We calculate moments of the $O(\alpha_s^3)$ heavy flavor contributions to the Wilson coefficients of the structure function $F_2(x,Q^2)$ in the region $Q^2\gg m^2$. The massive Wilson coefficients are obtained as convolutions of massive operator matrix elements (OMEs) and the known light flavor Wilson coefficients. The calculation of moments of the massive OMEs involves a first independent recalculation of moments of the fermionic contributions to all 3--loop anomalous dimensions of the unpolarized twist--2 local composite operators stemming from the light--cone expansion \cite{url}.