We show that for a large range of parameters in a SU(2)L×{}U(1) electroweak theory with two Higgs doublets there may exist classically stable flux tubes of Z boson magnetic field. In a limit of an extra global Ũ \~{U}{}(1) symmetry, these flux tubes become topologically stable. These results are automatically valid even if Ũ \~{U}{}(1) is gauged.
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Dvali et al. (1993) studied this question.
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