Neutral rho and A mesons in magnetic field in SU(2) lattice gauge theory

Correlators of vector, axial and pseudoscalar currents have been calculated in external strong magnetic field in SU(2) gluodynamics on the lattice. Neutral $\rho$ and $A$ meson masses with a zero spin projection to the axis parallel to the external magnetic field $B$ are calculated. The mass of the neutral $\rho$ meson with zero spin decreases with increasing of the magnetic field for available values of the magnetic field $eB\lesssim 2-2.5\, \Gev^2$, such behavior is necessary for a condensation of $\rho$ mesons in a strong magnetic field.