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.
Highlights
Understanding the internal structure of hadrons from first principles remains one of the foremost tasks in particle and nuclear physics
This allows for the Q2 dependence of the low moments of the nucleon structure functions to be studied in a lattice calculation for the first time
The usefulness of the operator product expansion (OPE) comes from the assumption that the nonperturbative physics is contained in the operator matrix elements, known as factorization, while the Wilson coefficients are calculable in perturbation theory
Summary
Understanding the internal structure of hadrons from first principles remains one of the foremost tasks in particle and nuclear physics. Lattice QCD calculations of nucleon structure functions have largely been limited to matrix elements of leading twist. The usefulness of the OPE comes from the assumption that the nonperturbative physics is contained in the operator matrix elements, known as factorization, while the Wilson coefficients are calculable in perturbation theory. This fundamental property is threatened by the presence of power divergences. We build upon a recent paper [12] outlining a procedure to determine nucleon structure functions from a lattice QCD calculation of the forward Compton amplitude.
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