Heavy Flavor DIS Wilson coefficients in the asymptotic regime

Abstract

We report on results for the heavy flavor contributions to $F_2(x,Q^2)$ in the limit $Q^2\gg m^2$ at {\sf NNLO}. By calculating the massive $3$--loop operator matrix elements, we account for all but the power suppressed terms in $m^2/Q^2$. Recently, the calculation of fixed Mellin moments of all $3$--loop massive operator matrix elements has been finished. We present new all--$N$ results for the $O(n_f)$--terms, thereby confirming the corresponding parts of the $3$--loop anomalous dimensions. Additionally, we report on first genuine $3$--loop results of the ladder--type diagrams for general values of the Mellin variable $N$.