On Spherically-symmetric Solutions in the Two-higgs Standard Model

We report the results of a numerical search for non-topological solitons in the two-Higgs standard model, characterized by the non-trivial winding, π3(S ), of the relative phase of the two doublets. In a region of (weak-coupling) parameter space we identify a branch of winding solutions, which are lower in energy than the embedded standard sphaleron and deformed (bi)sphalerons. Contrary, however, to what happens in 2d toy models, these solutions remain unstable even for very large Higgs masses. Two of us have analyzed recently non-topological winding solitons in renormalizable gauge models with two Higgs scalars. Such solitons arise in two and three space-time dimensions [1], and can be embedded as extended membrane defects in the weakly-coupled two-Higgs standard model (2HSM) [2]. It was furthermore argued by analogy [1] that the 2HSM may have stringlike or particle-like excitations characterized by a non-trivial mapping of the spatial three sphere onto the relative phase of the two doublets. Depending on the details of the potential, the relevant quantity could be either the Hopf invariant, π3(S ), or the winding number, π3(S ). Here we report the results of a numerical search for solitons of the latter type. The search revealed indeed a branch of winding solutions, but unlike their 2d analogs these stay classically unstable for arbitrarily large Higgs masses. These new solutions could nevertheless be of interest for the study of electroweak baryogenesis in the 2HSM [3]. Sphaleron solutions in the 2HSM have been discussed previously in ref. [4] and in a different context in ref. [5]. There exists a close analogy between sphaleron solutions in the minimal standard model [6, 7, 8], and those in the abelian-Higgs [10] or global doublewell [9] models on the circle. Similarly, the structure of classical solutions in the 2HSM is strongly reminiscent of that in the abelian two-Higgs, or in the global mexican-hat model on the circle. This latter model is defined by the action S = ∫