Heavy flavor operator matrix elements at $O(a_s^3)$

TL;DR

This work tackles heavy-quark corrections to unpolarized deep-inelastic scattering in the asymptotic regime $Q^2 \gg m^2$ by computing fixed NNLO (three-loop) moments of heavy-flavor operator matrix elements (OMEs). Using a rigorous diagrammatic approach and renormalization in the $\overline{\rm MS}$ and on-shell schemes, the authors obtain the moments for the fermionic sectors $A_{qq,Q}^{(3),{\sf NS,+}}$, $A_{Qq}^{(3),{\sf PS}}$, and $A_{gq,Q}^{(3)}$ for even $N$ in the range $N=2$ to $12$, validating the fermionic parts of the ${\sf NNLO}$ anomalous dimensions (ANDIMNSS). They confirm the pole structure from renormalization, observe the cancellation of $\zeta_2$ terms after renormalization, and identify a genuine mass-effect term $B_4$ in the constant pieces. This work sets the stage for fixed moments of heavy-flavor Wilson coefficients at ${\sf NNLO}$ in the $Q^2 \gg m^2$ limit and will improve precision in parton distribution function determinations.

Abstract

The heavy quark effects in deep--inelastic scattering in the asymptotic regime $Q^2 \gg m^2$ can be described by heavy flavor operator matrix elements. Complete analytic expressions for these objects are currently known to ${\sf NLO}$. We present first results for fixed moments at ${\sf NNLO}$. This involves a recalculation of fixed moments of the corresponding ${\sf NNLO}$ anomalous dimensions, which we thereby confirm.