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

Masahiro Kawasaki1,2,*, Kai Murai3,†, and Fuminobu Takahashi3,2,‡

  • 1ICRR, University of Tokyo, Kashiwa 277-8582, Japan
  • 2Kavli IPMU (WPI), UTIAS, University of Tokyo, Kashiwa 277-8583, Japan
  • 3Department of Physics, Tohoku University, Sendai, Miyagi 980-8578, Japan

  • *Contact author: kawasaki@icrr.u-tokyo.ac.jp
  • †Contact author: kai.murai.e2@tohoku.ac.jp
  • ‡Contact author: fumi@tohoku.ac.jp
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Phys. Rev. D 111, 123545 – Published 20 June, 2025

DOI: https://doi.org/10.1103/ykwz-4nrq

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.

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Phys. Rev. D 111, 123545– Published 20 June, 2025
  • Received 1 May 2025
  • Accepted 29 May 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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