Lattice QCD evaluation of the Compton amplitude employing the Feynman-Hellmann theorem

The forward Compton amplitude describes the process of virtual photon scattering from a hadron and provides an essential ingredient for the understanding of hadron structure. As a physical amplitude, the Compton tensor naturally includes all target mass corrections and higher twist effects at a fixed virtuality, $Q^2$. By making use of the second-order Feynman-Hellmann theorem, the nucleon Compton tensor is calculated in lattice QCD at an unphysical quark mass across a range of photon momenta $3 \lesssim Q^2 \lesssim 7$ GeV$^2$. This allows for the $Q^2$ dependence of the low moments of the nucleon structure functions to be studied in a lattice calculation for the first time. The results demonstrate that a systematic investigation of power corrections and the approach to parton asymptotics is now within reach.
Comment: 18 pages, 8 figures. Title has been changed due to the Editor's request. Version to appear in PRD