Knot soliton in Weinberg-Salam model

TL;DR

This paper numerically investigates a topological knot solution in the Weinberg-Salam model, demonstrating its relation to a Ginzburg-Landau type model and estimating its energy to be around 39 TeV.

Contribution

It introduces a numerical analysis of the electroweak knot solution using gauge-invariant projections and variational methods, linking it to a Ginzburg-Landau framework.

Findings

The knot energy is approximately 39 TeV.

The neutral boson and Higgs field form a stable knot configuration.

The restricted Lagrangian reduces to a Ginzburg-Landau model with hidden SU(2) symmetry.

Abstract

We study numerically the topological knot solution suggested recently in the Weinberg-Salam model. Applying the SU(2) gauge invariant Abelian projection we demonstrate that the restricted part of the Weinberg-Salam Lagrangian containing the interaction of the neutral boson with the Higgs scalar can be reduced to the Ginzburg-Landau model with the hidden SU(2) symmetry. The energy of the knot composed from the neutral boson and Higgs field has been evaluated by using the variational method with a modified Ward ansatz. The obtained numerical value is 39 Tev which provides the upper bound on the electroweak knot energy.