Existence of Double Vortex Solutions

We show analytically and numerically the existence of double vortex solutions in two-Higgs systems. These solutions are generalizations of the Nielsen-Olesen vortices and exist for all values of the parameters in the Lagrangians considered. We derive analytically the asymptotic behavior of the solutions and confirm it numerically by solving the field equations. Finally, we show that these solutions can be embedded in realistic theories like the two-doublet extension of the standard model. E-mail address: [email protected] Also, Visiting Scientist, Department of Physics, Brown University, Providence, R.I. 02912. It has recently been shown[1, 2] that the Nielsen-Olesen vortex solution[3, 4] can be embedded in the standard electroweak model. It was also shown[5] that the resulting electroweak vortices are dynamically (but not topologically) stable for a finite range of parameters of the electroweak model Lagrangian. This range of parameters however is not included within the limits allowed by current experiments, assuming the simplest form of the Higgs sector (one Higgs doublet). There are recent theoretical and experimental indications[6] that the Higgs sector of the standard model may need to be extended to involve at least two Higgs multiplets for the electroweak symmetry breaking. This is required, for example, in order to achieve consistent unification of the gauge couplings on high energy scales[6]. The prospect of this possibility raises the question of what (if any) soliton-like objects exist in these extended, multiple Higgs theories. Clearly the Nielsen-Olesen vortex which involves a single Higgs can not be directly embedded in multiple Higgs systems unless it is generalized first. Recent studies[7] have shown the existence of an extra global symmetry in realistic two-Higgs doublet models, which breaks during the electroweak symmetry breaking. The breaking of this extra symmetry may lead to topologically stable embedded double vortices (the term ‘double’ here refers to the number of Higgs fields that wind non-trivially and not to the topological charge or the flux of the vortices). It is therefore important to study how can the Nielsen-Olesen vortex be generalized to multiple Higgs systems, what are the properties of the new solutions and how can they be embedded in realistic two doublet models. These issues consist the focus of the present work. Previous studies [8] attempting to generalize the Nielsen-Olesen solution have claimed that such generalized solutions exist only for certain values of the parameters of the two-Higgs Lagrangian. These studies, which did not make any numerical confirmation of their results, used a very constraining ansatz for the asymptotic behavior of their candidate solutions which led to incorrect conclusions about the existence of solutions. Here, we avoid the use of any ansatz and show that vortex solutions exist for any value of parameters in the Lagrangian. We derive the asymptotic behavior of these solutions and point out new features that are not present in the Nielsen-Olesen vortices. We also obtain the solutions numerically and confirm the derived asymptotic behavior. Finally, we consider the realistic