A Method to Extract Charged Hadron Properties from Lattice QCD in Magnetic Fields

TL;DR

This paper introduces a projection method to extract magnetic properties of charged hadrons from lattice QCD in magnetic fields, addressing challenges posed by Landau levels and finite volume effects.

Contribution

A simple projection technique for isolating the lowest Landau level in lattice QCD calculations of charged hadrons' magnetic properties.

Findings

The projection technique effectively isolates the lowest Landau level.

Discretization effects can be treated perturbatively.

Finite volume effects depend on magnetic flux quantum, not lattice volume.

Abstract

By analyzing the external field dependence of correlation functions, the magnetic properties of hadrons can be determined using lattice QCD in magnetic fields. To compute the magnetic moments and polarizabilities of charged hadrons, for example, one requires sufficiently weak magnetic fields. Such field strengths, however, lead to closely spaced Landau levels that are not straightforwardly resolved using standard lattice spectroscopy. Focusing on charged spinless hadrons, we introduce a simple projection technique that can be used to isolate the lowest Landau level. As the technique requires the explicit coordinate-space wave-function, we investigate the extent to which the continuum, infinite volume wave-function can be employed. We find that, in practice, the effects of discretization can be handled using a perturbative expansion about the continuum. Finite volume corrections are taken into account by using the discrete magnetic translational invariance of the torus. We show that quantized magnetic fields can lead to pernicious volume effects which depend on the magnetic flux quantum, rather than on the lattice volume.