$\pi^{\pm}$- and $\rho^{0,\pm}$-mesons in a strong magnetic field on the lattice

We calculated the correlators of pseudoscalar and vector currents in external strong abelian magnetic field in $SU(3)$ gluodynamics. From the correlation functions we obtain the ground state energies (masses) of neutral $\rho^0$-meson and charged $\pi^{\pm}$- and $\rho^{\pm}$-mesons. The energy of the $\rho^0$-meson with zero spin projection on the axis of the field decreases, while the energies with non-zero spins increase with the field value. The mass of charged $\pi^{\pm}$-mesons increases with the field. We observe the agreement between Landau level picture and behaviour of charged $\rho^{\pm}$-mesons for moderate magnetic fields. There are no evidences in favour of charged vector meson condensation or tachyonic mode existence at large magnetic fields. The $g$-factor of $\rho^{\pm}$ is estimated in the chiral limit.