Dependence of Lattice Hadron Masses on External Magnetic Fields

TL;DR

This paper investigates how external magnetic fields influence lattice hadron masses, identifying key factors affecting results and confirming linear mass behavior, while improving measurements of nucleon magnetic moments.

Contribution

It provides new insights into the dependence of hadron masses on magnetic fields and refines lattice measurement techniques for nucleon magnetic moments.

Findings

Qualitative confirmation of linear mass behavior with magnetic field

Identification of boundary discontinuities affecting simulations

Improved measurements of nucleon magnetic moments

Abstract

We study the variation of the hadron masses in the presence of external magnetic fields of strength of the order of the masses themselves. We identify the main factors affecting the lattice simulation results: - the boundary discontinuities for $eB << 2\pi / L^2 a^2$. - the SU(6) choice of the hadron wave-function. We confirm qualitatively the earlier theoretical ansatz on the linear behaviour of the masses with the magnetic field and, as a by-product, we improve the lattice measurements of the nucleon magnetic moments. However our systematic and statistical errors preclude us from measuring the theoretically predicted field strength at which the proton becomes heavier than the neutron.