New Results on the 3-Loop Heavy Flavor Wilson Coefficients in Deep-Inelastic Scattering

Abstract

We report on recent results obtained for the 3-loop heavy flavor Wilson coefficients in deep-inelastic scattering (DIS) at general values of the Mellin variable $N$ at larger scales of $Q^2$. These concern contributions to the gluonic ladder-topologies, the transition matrix elements in the variable flavor scheme of $O(n_f T_F^2)$ and $O(T_F^2)$, and first results on higher 3-loop topologies. The knowledge of the heavy flavor Wilson coefficients at 3-loop order is of importance to extract the parton distribution functions and $α_s(M_Z^2)$ in complete NNLO QCD analyses of the world precision data on the structure function $F_2(x,Q^2)$.

Figures (4)

• Figure 1: 3-loop ladder diagram containing a central local operator insertion.
• Figure 2: A 3-loop Benz diagram.
• Figure 3: A second example of a 3-loop Benz topology.
• Figure 4: A 3-loop graph containing two massive fermion lines $m_1=m_2$ and an operator insertion.