Stability of electroweak strings

We map the parameter space that leads to stable $Z$ vortices in the electroweak model. For ${sin}^2{\theta }_W=0.23\mathrm{}$, we find that the strings are unstable for a Higgs-boson mass larger than 24 GeV. Given the latest constraints on the Higgs-boson mass from the CERN $e^{+}{e}^{-}$ collider LEP, this shows that, if the standard electroweak model is realized in nature, the $Z$ vortex (in the bare model) is unstable.