The Evolution of Meson Masses in a Strong Magnetic Field

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.