First $O(\alpha_s^3)$ heavy flavor contributions to deeply inelastic scattering

TL;DR

This paper computes the last missing two-loop contributions to heavy flavor Wilson coefficients in deep-inelastic scattering at order (), enhancing the precision of theoretical predictions in the asymptotic regime.

Contribution

It provides the first complete three-loop results for heavy flavor contributions in unpolarized deep-inelastic scattering, including new terms proportional to T_F^2 in Mellin space.

Findings

Calculated the last two-loop renormalization contributions at three loops.

Derived the () heavy flavor Wilson coefficients.

Obtained parts of the NNLO anomalous dimensions.

Abstract

In the asymptotic limit $Q^2 \gg m^2$, the heavy flavor Wilson coefficients for deep--inelastic scattering factorize into the massless Wilson coefficients and the universal heavy flavor operator matrix elements resulting from light--cone expansion. In this way, one can calculate all but the power corrections in $(m^2/Q^2)^k, k > 0$. The heavy flavor operator matrix elements are known to ${\sf NLO}$. We present the last 2--loop result missing in the unpolarized case for the renormalization at 3--loops and first 3--loop results for terms proportional to the color factor $T_F^2$ in Mellin--space. In this calculation, the corresponding parts of the ${\sf NNLO}$ anomalous dimensions \cite{LARIN,MVVandim} are obtained as well.