Dangerous skyrmions in little Higgs models

Skyrmions are present in many models of electroweak symmetry breaking where the Higgs is a pseudo-Goldstone boson of some strongly interacting sector. They are stable, composite objects whose mass lies in the range 10-100 TeV and can be naturally abundant in the universe due to their small annihilation cross-section. They represent therefore good dark matter candidates. We show however in this work that the lightest skyrmion states are electrically charged in most of the popular little Higgs models, and hence should have been directly or indirectly observed in nature already. The charge of the skyrmion under the electroweak gauge group is computed in a model-independent way and is related to the presence of anomalies in the underlying theory via the Wess-Zumino-Witten term.