The Gluonic Operator Matrix Elements at O(\alpha_s^2) for DIS Heavy Flavor Production

TL;DR

This paper computes the two-loop gluonic operator matrix elements relevant for heavy flavor production in deep inelastic scattering, aiding the precise determination of parton distribution functions in the variable flavor number scheme.

Contribution

It provides the explicit calculation of $O(\alpha_s^2)$ gluonic operator matrix elements, including linear epsilon terms, crucial for higher-order corrections in DIS heavy flavor analysis.

Findings

Calculated $O(\alpha_s^2)$ gluonic operator matrix elements.

Included linear epsilon terms for higher-order accuracy.

Discussed implications for fixed and variable flavor schemes.

Abstract

We calculate the $O(\alpha_s^2)$ gluonic operator matrix elements for the twist--2 operators, which contribute to the heavy flavor Wilson coefficients in unpolarized deeply inelastic scattering in the region $Q^2 \gg m^2$, up to the linear terms in the dimensional parameter $\varepsilon$, ($D= 4 + \varepsilon$). These quantities are required for the description of parton distribution functions in the variable flavor number scheme (VFNS). The $O(\alpha_s^2 \varepsilon)$ terms contribute at the level of the $O(\alpha_s^3)$ corrections through renormalization. We also comment on additional terms, which have to be considered in the fixed (FFNV) and variable flavor number scheme, adopting the $\overline{\rm MS}$ scheme for the running coupling constant.