Two--Loop Massive Operator Matrix Elements for Unpolarized Heavy Flavor Production to $O(\epsilon)

TL;DR

This paper computes two-loop massive operator matrix elements for unpolarized heavy flavor production in deep inelastic scattering, including $O( ext{ extbackslash epsilon})$ terms, advancing precision in theoretical predictions.

Contribution

It introduces a novel calculation of $O( ext{ extbackslash alpha}_s^2)$ operator matrix elements using light-cone expansion and hypergeometric functions, without integration-by-parts.

Findings

Derived explicit expressions for operator matrix elements

Expressed results in terms of nested harmonic sums

Enhanced the accuracy of heavy flavor Wilson coefficient calculations

Abstract

We calculate the $O(\alpha_s^2)$ massive 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 $O(\epsilon)$ contributions. These terms contribute through the renormalization of the $O(\alpha_s^3)$ heavy flavor Wilson coefficients of the structure function $F_2(x,Q^2)$. The calculation has been performed using light--cone expansion techniques without using the integration-by-parts method. We represent the individual Feynman diagrams by generalized hypergeometric structures, the $\epsilon$--expansion of which leads to infinite sums depending on the Mellin variable $N$. These sums are finally expressed in terms of nested harmonic sums using the general summation techniques implemented in the {\tt Sigma} package.