Two-Loop Massive Operator Matrix Elements and Unpolarized Heavy Flavor Production at Asymptotic Values Q^2 >> m^2

TL;DR

This work computes the unpolarized two-loop massive operator matrix elements in the asymptotic DIS regime Q^2 >> m^2, enabling the heavy-flavor Wilson coefficients for F_2 at O(α_s^2) and F_L at O(α_s^3). By performing the calculation directly in Mellin space without integration-by-parts, the authors obtain compact analytic expressions in terms of harmonic sums, and verify consistency with earlier results by Buza et al. The methodology relies on factorization into light-flavor Wilson coefficients and massive OMEs, with renormalization handled in the MSbar scheme and mass on-shell. The results yield analytic, quickly invertible Mellin-space representations suitable for fast x-space phenomenology and provide a comprehensive toolkit of sums (Appendices A and B) that are broadly useful for higher-order QCD calculations.

Abstract

We calculate the $O(α_s^2)$ massive operator matrix elements for the twist--2 operators, which contribute to the heavy flavor Wilson coefficients in unpolarized deeply inelastic scattering in the region $Q^2 \gg m^2$. The calculation has been performed using light--cone expansion techniques. We confirm an earlier result obtained in \cite{Buza:1995ie}. The calculation is carried out without using the integration-by-parts method and in Mellin space using harmonic sums, which lead to a significant compactification of the analytic results derived previously. The results allow to determine the heavy flavor Wilson coefficients for $F_2(x,Q^2)$ to $O(α_s^2)$ and for $F_L(x,Q^2)$ to $O(α_s^3)$ for all but the power suppressed terms $\propto (m^2/Q^2)^k, k \geq 1$.

Figures (5)

• Figure 1: Feynman rules for the operator insertion $\otimes$ to $O(a_s^2)$, cf. FLO. $\Delta$ denotes a light--like vector, $\Delta.\Delta = 0$.
• Figure 2: The Feynman diagrams contribution to the operator matrix element $A_{Qg}$ at $O(a_s)$. Weavy lines denote gluons, and the full arrow lines are the heavy quark lines. The Feynman rules for the operator insertions are given in Figure \ref{['fig:1']}.
• Figure 3: The diagrams contributing to the operator matrix element $A_{Qg}$ at $O(a_s^2)$. Weavy lines denote gluons, dashed lines ghosts, and the full arrow lines are the heavy quark lines. The Feynman rules for the operator insertions are given in Figure \ref{['fig:1']}.
• Figure 4: The diagrams contributing to the operator matrix element $A_{Qq}^{\rm PS}$ at $O(a_s^2)$. Weavy lines denote gluons, the thick full arrow lines are the heavy quark lines, and the thin full lines are light quark lines. The Feynman rules for the operator insertions are given in Figure \ref{['fig:1']}.
• Figure 5: The diagrams contributing to the operator matrix element $A_{Qqq}^{\rm NS}$ at $O(a_s^2)$. Weavy lines denote gluons, the full arrow lines are the heavy quark lines, and the thin full lines are light quark lines. The Feynman rules for the operator insertions are given in Figure \ref{['fig:1']}.