The evolution of meson masses in a strong magnetic field

Spectra of q (q) over bar 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.