Decay of Z-string due to the fermion emission

The question of classical topological stability of the gauge vortex defects is reanalyzed upon taking into account the quantum perturbative effects. The purely Abelian Higgs string remains stable while the coupling of the effectively Abelian Z-string (with the fixed zero upper component of the scalar doublet) to the fermions of the minimal standard model is shown to result in its decay, via the fermionic pair emission. The decay rate is scaled as $10^{-1}$ of the decay rate of $Z^0$ boson. The influence of the surrounding charge-asymmetric fermionic matter is considered, demonstrating the dependence of the decay rate on the contour shape and its suppression at sufficiently large charge asymmetry.