We study the existence of skyrmions in the presence of all the electroweak degrees of freedom, including a dynamical Higgs boson, with the electroweak symmetry being non-linearly realized in the scalar sector. For this, we use the formulation of the Higgs Effective Field Theory (HEFT). In contrast with the linear realization, a well-defined winding number exists in HEFT for all scalar field configurations. We classify the effective operators that can potentially stabilize the skyrmions and numerically find the region in parameter spaces that support them. We do so by minimizing the static energy functional using neural networks. This method allows us to obtain the minimal-energy path connecting the vacuum to the skyrmion configuration and calculate its mass and radius. Since skyrmions are not expected to be produced at colliders, we explore the experimental and theoretical bounds on the operators that generate them. Finally, we briefly consider the possibility of skyrmions being dark matter candidates.
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