Heavy flavor operator matrix elements at $O(a_s^3)$

Understand

The heavy quark effects in deep--inelastic scattering in the asymptotic regime $Q^2 \gg m^2$ can be described by heavy flavor operator matrix elements.

• Complete analytic expressions for these objects are currently known to ${\sf NLO}$.
• We present first results for fixed moments at ${\sf NNLO}$.
• This involves a recalculation of fixed moments of the corresponding ${\sf NNLO}$ anomalous dimensions, which we thereby confirm.