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

TL;DR

This paper uses lattice QCD and the Feynman-Hellmann theorem to compute the nucleon Compton amplitude across various photon momenta, enabling the study of structure functions and power corrections at different $Q^2$ values.

Contribution

It introduces a novel lattice QCD method employing the Feynman-Hellmann theorem to evaluate the Compton tensor and analyze the $Q^2$ dependence of nucleon structure functions.

Findings

First lattice QCD calculation of the $Q^2$ dependence of low moments of structure functions.

Demonstrates the feasibility of studying power corrections and asymptotic behavior systematically.

Provides insights into target mass corrections and higher twist effects at fixed virtuality.

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 $3 \lesssim Q^2 \lesssim 7$ 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.