The magnetic polarizabilities and

Study of the ground state energies of neutral and charged vector meson was performed in SU(3) lattice gauge theory in the strong abelian magnetic field. Our method allows us to distinguish the ground state energy of mesons for various spin projections on the axis of the external magnetic field . We are observe the splitting the ground state energy of ρ mesons depending on spin projections: for neutral ρ0 meson with zero spin projection on the axis of the field ground state energy decreases, while the energies with non-zero spins increase with the field value. For charged ρ± mesons we observe the agreement between Landau level picture and our data at magnetic field less then 0.6GeV2. The magnetic polarizabilities of vector mesons were found for the lattice volume 184 fitting the ground state energies. We found the g-factor of ρ± in the chiral limit. This value is compatible with experimental determination and theoretical value from relativistic quark model