Yu. A. Simonov, B. O. Kerbikov, M. A. Andreichikov
We study the relativistic quark-antiquark system embedded in magnetic field (MF). The Hamiltonian containing confinement, color Coulomb and spin-spin interaction is derived. We analytically follow the evolution of the lowest neutral meson state as a function of MF strength. Calculating the color Coulomb energy $V_{Coul}$ we have observed the unbounded negative (at least in the limit of large $N_c$) contribution at large MF which makes the mass negative for $eB> eB^{QCD}_{crit}$. We display the $\pi^0$ and $\rho^0$ masses as functions of MF in comparison with recent lattice data.
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http://arxiv.org/abs/1210.0227
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