Logarithmic $O(α_s^3)$ contributions to the DIS Heavy Flavor Wilson Coefficients at $Q^2 \gg m^2$

TL;DR

The paper addresses the need for NNLO precision in heavy-flavor corrections to DIS by deriving the logarithmic $O(\alpha_s^3)$ contributions to massive operator matrix elements in the asymptotic region. It expresses the heavy-flavor Wilson coefficients as convolutions of massive OMEs with massless coefficients and provides explicit $N$-dependent results for the $A_{Qg}^{(3)}(N)$ matrix element in the $\overline{MS}$ scheme, including the leading $\ln^3$, $\ln^2$, and $\ln$ terms. The coefficients are built from 3-loop anomalous dimensions, lower-order OMEs, and harmonic sums up to weight 3, highlighting the interplay between logarithmic and constant terms in phenomenologically relevant kinematics. Overall, these results enhance the NNLO predictive power for structure functions involving heavy flavors and inform precise determinations of $\alpha_s$ and parton distributions. The work thus advances the theoretical control of heavy-flavor contributions in deep-inelastic scattering in the high-$Q^2$ limit.

Abstract

The logarithmic contributions to the massive twist-2 operator matrix elements for deep-inelastic scattering are calculated to $O(α_s^3)$for general values of the Mellin variable $N$.