Magnetic polarizabilities of light mesons in $SU(3)$ lattice gauge   theory
  We investigate the masses (ground state energies) of neutral pseudoscalar and vector meson in $SU(3)$ lattice gauge theory in strong abelian magnetic field. The energy of $\rho^0$ meson with zero spin projection $s_z=0$ on the axis of the external magnetic field decreases, while the energies with non-zero spins $s_z=-1$ and $+1$ increase with the field. The energy of $\pi^0$ meson decrease as a function of the magnetic field. We calculated the magnetic polarizabilities of pseudoscalar and vector mesons for lattice volume $18^4$. For $\rho^0$ with spin $|s_z|=1$ and $\pi^0$ meson the extrapolations to zero lattice spacing have been done. We do not observe any evidence in favour of tachyonic mode existence. 
E.V. Luschevskaya, O.E. Solovjeva, O.A. Kochetkov, O.V. Teryaev
hep-lat