On the Stability of Electroweak Strings (New Version)
  We map the parameter space that leads to stable Z-vortices in the electroweak model. For $sin^2 \theta_W = 0.23$, we find that the strings are unstable for a Higgs mass larger than 24 GeV. Given the latest constraints on the Higgs mass from LEP, this shows that, if the standard electroweak model is realized in Nature, the Z-vortex (in the bare model) is unstable. 
M. James, L. Perivolaropoulos and T. Vachaspati