Higher order corrections to heavy flavour production in deep inelastic scattering

TL;DR

The paper addresses heavy flavour production in deep inelastic scattering in the asymptotic regime $Q^2 \gg m^2$, showing that heavy flavour Wilson coefficients factorize into massless coefficients and massive operator matrix elements. It presents methods to obtain $O(\varepsilon)$ two-loop contributions and initiates three-loop calculations by developing an analytic framework in Mellin space, including cross-checks via Mellin-Barnes and hypergeometric approaches and a path to fixed-N three-loop results. Key contributions include the first $O(\varepsilon)$ results for unpolarized OMEs, an all-order $\varepsilon$ result for $A_{gg}^{(3)}$, and the setup for extensive three-loop computations using MATAD, with initial efforts on the dominant TF^2 color structures. The work advances toward a complete $O(\alpha_s^3)$ description of heavy flavour corrections, enabling improved predictions for DIS structure functions $F_2$ and $F_L$ in the high-$Q^2$ regime.

Abstract

In the asymptotic limit $Q^2 \gg m^2$, the non-power corrections to the heavy flavour Wilson coefficients in deep--inelastic scattering are given in terms of massless Wilson coeffcients and massive operator matrix elements. We start extending the existing NLO calculation for these operator matrix elements by calculating the O($ε$) terms of the two--loop expressions and having first investigations into the three--loop diagrams needed to O($α_s^3$).