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We investigate the ground state energies of vector $\rho^{\pm}$ and $K^{\pm*}$ mesons depending on the magnetic field value in the $SU(3)$ lattice gaugetheory. It has been shown that the energy of a vector particle depends on itsspin projection on the field axis. The magnetic dipole polarizability andhyperpolarizabilities give significant contributions to the energy value whichprevents the formation of the charged vector meson condensate at high magneticfields. We calculate the g-factor of $\rho^{\pm}$ and $K^{\pm*}$ mesons and thedipole magnetic polarizability of $\rho^{\pm}$ mesons.

Determination of the properties of vector mesons in external magnetic field by Quenched $SU(3)$ Lattice QCD