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

Isabella Bierenbaum; Johannes Blümlein; Sebastian Klein; Carsten Schneider

Paper

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

Abstract

We calculate the

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

, up to the

contributions. These terms contribute through the renormalization of the

heavy flavor Wilson coefficients of the structure function

. 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

--expansion of which leads to infinite sums depending on the Mellin variable

. These sums are finally expressed in terms of nested harmonic sums using the general summation techniques implemented in the {\tt Sigma} package.