Heavy Flavor DIS Wilson coefficients in the asymptotic regime

TL;DR

This work delivers the first all-$N$ results for the $n_f$-dependent parts of heavy-flavor 3-loop operator matrix elements in the asymptotic regime $Q^2\gg m^2$, enabling NNLO heavy-flavor Wilson coefficients for $F_2(x,Q^2)$. It combines the factorization of heavy-quark Wilson coefficients into massive OMEs and massless Wilson coefficients, integrates fixed Mellin-moment calculations with general $N$ results, and confirms the $3$-loop anomalous dimensions through independent computation. The study documents the harmonic-sum structure up to weight 4 and investigates ladder-type diagrams, including Appell-function representations for certain topologies, highlighting the mathematical complexity of 3-loop heavy-flavor corrections. These results provide essential input for precise DIS analyses and for variable-flavor-number schemes at colliders, improving predictions for processes involving heavy quarks at high scales.

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 $N$.

Figures (3)

• Figure 1: Examples for $3$--loop diagrams $\propto~n_f$. Solid lines: heavy quarks, dashed lines: light quarks, curly lines: gluons. $\otimes$: operator insertion.
• Figure 2: $3$--loop ladder tadpole. $\nu_i$ denote exponents of the propagators.
• Figure 3: Example $3$--loop ladder diagram.