Heavy Flavor Contributions to DIS Structure Functions at $O(\alpha_s^3)$

TL;DR

This paper computes third-order QCD corrections to heavy flavor contributions in deep inelastic scattering, enhancing theoretical precision for structure functions at high energy scales.

Contribution

It provides the first independent calculation of moments of fermionic contributions to three-loop anomalous dimensions and general Mellin variable expressions for massive operator matrix elements.

Findings

Calculated moments of heavy flavor Wilson coefficients at O(α_s^3)

Recalculated moments of fermionic contributions to three-loop anomalous dimensions

Expressions for massive operator matrix elements for general Mellin N

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. The expressions for the massive OMEs are now known for general values of the Mellin variable $N$ apart of one coefficient in the constant term, for which only a series of moments is computed.