Reconciling the lattice background field method with nonrelativistic QED: Spinor case

TL;DR

This paper resolves inconsistencies between lattice QCD background field methods and effective field theory by augmenting nonrelativistic QED with equations of motion operators, enabling better analysis of hadron responses in external fields.

Contribution

It introduces a hybrid framework combining relativistic hadron theory with nonrelativistic QED power counting for improved lattice QCD correlation function analysis.

Findings

Resolved background field method inconsistencies with EFT matching.

Derived new results for charged spin-half hadrons in magnetic fields.

Proper treatment of Landau levels in finite and infinite volumes.

Abstract

We show that inconsistency between background field methods, which are relevant for lattice QCD spectroscopy, and effective field theory matching conditions, which are obtained from scattering amplitudes, can be resolved by augmenting nonrelativistic QED with operators related by the equations of motion. To determine the coefficients of such operators, we perform the nonrelativistic expansion of QED for a spin-half hadron including non-minimal electromagnetic couplings. As an effective field theory framework could provide a valuable tool to analyze lattice QCD correlation functions in external fields, we investigate whether nonrelativistic QED can be used to this end. We argue, however, that the most desirable approach is a hybrid one, which combines a relativistic hadron theory with operator selection based on nonrelativistic QED power counting. In this hybrid framework, new results are obtained for charged spin-half hadrons in uniform magnetic fields, including a proper treatment of Landau levels both in infinite volume and on a torus.