Q -balls under a spontaneously broken U(1) symmetry

Abstract

We study the evolution of Q -balls under a spontaneously broken global U(1) symmetry. Q -balls are stabilized by the conservation of U(1) charge, but when the symmetry is spontaneously broken, the resulting Nambu-Goldstone boson can carry charge away from the Q -ball, potentially leading to charge leakage. To study this process in a controlled setting, we consider a scenario where Q -balls first form under an unbroken U(1) symmetry, which is then spontaneously broken. We introduce two complex scalar fields: one responsible for forming the Q -ball, and the other for spontaneously breaking the U(1) symmetry, allowing us to clearly separate the formation and symmetry-breaking phases. Using numerical simulations in a spherically symmetric system, we find that the evolution of Q -balls depends sensitively on the structure of the interaction between the two fields and the magnitude of symmetry breaking. Depending on parameters, Q -balls can completely decay, evaporate into smaller, stable Q -balls, or transition into oscillons/I-balls. In particular, we find that stable, localized remnants often survive the evolution over long timescales, especially when the symmetry-breaking scale is small. These results demonstrate that, even though spontaneous U(1) breaking can lead to significant energy and charge loss from Q -balls, stable localized objects with reduced or no charge can frequently survive and potentially contribute to cosmological relics.