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

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 $O(ϵ)$ 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 $ϵ$--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.

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