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

TL;DR

This paper presents new 3-loop heavy flavor Wilson coefficients for deep-inelastic scattering, enhancing the precision of parton distribution functions and strong coupling constant extractions in NNLO QCD analyses.

Contribution

It provides the first results for 3-loop heavy flavor Wilson coefficients at general Mellin N, including contributions to gluonic topologies and transition matrix elements.

Findings

Results for 3-loop heavy flavor Wilson coefficients at general N

Insights into gluonic ladder-topologies contributions

Initial findings on higher 3-loop topologies

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 $\alpha_s(M_Z^2)$ in complete NNLO QCD analyses of the world precision data on the structure function $F_2(x,Q^2)$.