Lattice QCD evaluation of the Compton amplitude employing the Feynman-Hellmann theorem
Kadir Utku Can, A. Hannaford-Gunn, R. Horsley, Y. Nakamura, H. Perlt, P. E. L. Rakow, G. Schierholz, Kim Somfleth, H. Stüben, R. D. Young, J. M. Zanotti
Abstract
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 $3\ensuremath{\lesssim}{Q}^{2}\ensuremath{\lesssim}7\text{ }\text{ }{\mathrm{GeV}}^{2}$. 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.