The Compton Amplitude, lattice QCD and the Feynman-Hellmann approach

TL;DR

This paper develops a second-order Feynman-Hellmann method for lattice QCD to compute hadronic matrix elements more efficiently, focusing on the Compton amplitude and scattering processes, with promising preliminary results.

Contribution

It introduces a second-order perturbative Feynman-Hellmann approach for lattice QCD, enabling the calculation of the Compton amplitude and scattering without three- or four-point functions.

Findings

Numerical results demonstrate the method's potential effectiveness.

The approach simplifies calculations of hadronic matrix elements.

Preliminary results suggest promising accuracy and efficiency.

Abstract

A major objective of lattice QCD is the computation of hadronic matrix elements. The standard method is to use three-point and four-point correlation functions. An alternative approach, requiring only the computation of two-point correlation functions is to use the Feynman-Hellmann theorem. In this talk we develop this method up to second order in perturbation theory, in a context appropriate for lattice QCD. This encompasses the Compton Amplitude (which forms the basis for deep inelastic scattering) and hadron scattering. Some numerical results are presented showing results indicating what this approach might achieve.