Lattice QCD calculation of the Compton amplitude subtraction function

TL;DR

This paper employs lattice QCD and the Feynman-Hellmann method to directly compute the Compton amplitude subtraction function, reducing uncertainties and controlling systematic errors, thus enabling more precise, model-independent determinations relevant to proton structure puzzles.

Contribution

It introduces a novel lattice QCD approach using the Feynman-Hellmann method to determine the subtraction function and addresses discretisation artefacts, improving accuracy over previous methods.

Findings

Good agreement with continuum OPE expectations.

Controlled discretisation artefacts reduce systematic errors.

Applicable over a wide range of kinematic scales.

Abstract

The Compton amplitude subtraction function is an essential component in work concerning both the proton radius puzzle and the proton-neutron mass difference. However, owing to the difficulty in determining the subtraction function, it remains a key source of uncertainty in these two contexts. Here, we use the Feynman-Hellmann method to determine this subtraction function directly from lattice QCD. Furthermore, we demonstrate how to control dominant discretisation artefacts for this calculation, eliminating a major source of systematic error. This calculation is performed for a range of hard momentum scales, and three different sets of gauge configurations for pion masses about 400 MeV. Our results show good agreement with continuum OPE expectations. As such, this work paves the way for model-independent and precise determinations of the subtraction function over a wide range of kinematics.