The Evolution of Meson Masses in a Strong Magnetic Field

TL;DR

This paper investigates how meson masses, specifically $ ho$ and $ ho$ mesons, evolve under strong magnetic fields using a relativistic Hamiltonian approach, providing analytical and lattice numerical insights.

Contribution

It introduces a relativistic Hamiltonian framework to analyze meson spectra in magnetic fields, combining analytical and lattice methods for comprehensive results.

Findings

Identifies three characteristic behaviors of meson mass splittings in magnetic fields.

Provides analytical predictions validated by lattice simulations.

Demonstrates agreement between theory and numerical results across different spin states.

Abstract

Spectra of $q \bar{q}$ hadrons are investigated in the framework of the Hamiltonian obtained from the relativistic path integral in external homogeneous magnetic field. The spectra of all 12 spin-isospin s-wave states, generated by $\pi$ and $\rho$ mesons with different spin projections, are studied both analytically and numerically on the lattice as functions of (magnetic field) $eB$. Results are in agreement and demonstrate three types of behavior, with characteristic splittings predicted by the theory.