Quark-Antiquark System in Ultra-Intense Magnetic Field

Abstract

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 $eB>e{B}_{crit}^{QCD}$. We display the ${\pi }^0$ and ${\rho }^0$ masses as functions of MF in comparison with recent lattice data.

16 pages, 1 figure