Background field Landau mode operators for the nucleon

TL;DR

This paper introduces new quark operators based on Laplacian eigenmodes to improve the calculation of nucleon energy shifts in magnetic fields, enabling more precise determination of magnetic properties.

Contribution

The paper presents a novel operator construction using Laplacian eigenmodes to better isolate nucleon signals in magnetic backgrounds, improving upon standard methods.

Findings

Enhanced precision in nucleon energy shift calculations

Preliminary neutron and proton magnetic polarizability results

Demonstration of operator effectiveness in magnetic fields

Abstract

The introduction of a uniform background magnetic field breaks three-dimensional spatial symmetry for a charged particle and introduces Landau mode effects. Standard quark operators are inefficient at isolating the nucleon correlation function at nontrivial field strengths. We introduce novel quark operators constructed from the two-dimensional Laplacian eigenmodes that describe a charged particle on a finite lattice. These eigenmode-projected quark operators provide enhanced precision for calculating nucleon energy shifts in a magnetic field. Preliminary results are obtained for the neutron and proton magnetic polarisabilities using these methods.