A W–dressed Electroweak String

We give plausibility arguments for the existence of a W–dressed electroweak string for the Weinberg–Salam model with θW = 0. This string is a Z–string which in the core has a finite energy contribution from W–condensation induced by the anomalous magnetic moment in the Yang–Mills field. The solution which has minimum energy at r = 0 interpolates between the unbroken (r = 0) and the broken (r → ∞) SU(2)× Uy(1) phase. Recently it has been shown by Vachaspati [1] that the electroweak Weinberg–Salam theory [2] has vortex solutions. This solution is formed from the lower component of the Higgs field and the Z field, and it satisfies the usual vortex equations of motion [3]. These electroweak strings are not stable on topological grounds, and hence their stability must be investigated. This was done [4], and stability was found for a range of parameters unfortunately not within the experimental limits. It has been suggested [5] that perhaps the inclusion of at least two Higgs multiplets may improve this situation. It has, however, been pointed out by Perkins [6] that the electroweak string can have its energy lowered by the formation of a W–condensate in its core. This is because of the fact that the electroweak vacuum is unstable to the formation of a W–condensate [7] if a strong “magnetic” Z–field is applied. The physical reason for this effect is that the electroweak vacuum is “paramagnetic”, with an energy which contains the terms − cos θWB Z μ + μ , (1) where B i = 1 2 εijkZjk and the magnetic moment density μ is given by