[en] The asymptotics of the renorminvariant mass of the charged vector boson in a constant magnetic field near the tachyon state threshold H → H₀ is calculated in the gauge theory with spontaneous SU(2) → U(1) symmetry breaking. The part played by the radiative effects in appearance of the tachyon instability is estimated. In the Yang-Mills massless theory limit the radiative corrections make the vacuum stable, which fact indicates the absence of the tachyon. In this case, a possible phase transition is due to the growth of the effective charge and mass of the vector particle in the field. For sufficiently light Higgs particles inclusion of radiative corrections shifts the instability threshold to the fields Hsub(cr) < H₀ where the perturbation theory can be reliably applied. Parameters of the arising condensate of vector particles are studied