First $O(\hat{I}{\pm }_s^3)$ heavy flavor contributions to deeply inelastic scattering

Abstract

In the asymptotic limit $Q^2\gg m^2$, the heavy flavor Wilson coefficients for deep--inelastic scattering factorize into the massless Wilson coefficients and the universal heavy flavor operator matrix elements resulting from light--cone expansion. In this way, one can calculate all but the power corrections in $(m^2/Q^2{)}^k,k>0$. The heavy flavor operator matrix elements are known to $\mathsf{NLO}$. We present the last 2--loop result missing in the unpolarized case for the renormalization at 3--loops and first 3--loop results for terms proportional to the color factor $T_F^2$ in Mellin--space. In this calculation, the corresponding parts of the $\mathsf{NNLO}$ anomalous dimensions \cite{LARIN,MVVandim} are obtained as well.

6 pages, Contribution to the Proceedings of "Loops and Legs in Quantum Field Theory", 2008, Sondershausen, Germany, and DIS 2008, London, UK