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Multifield oscillons/I-balls in the Friedberg-Lee-Sirlin model

Kai Murai1,2, Tatsuya Ogawa2,3,4, and Fuminobu Takahashi2,5

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Phys. Rev. D 114, 036019 – Published 17 August, 2026

DOI: https://doi.org/10.1103/gslh-lb7k

Abstract

We study oscillon/I-ball solutions in a real scalar version of the Friedberg-Lee-Sirlin model. Using the multiple-scale analysis, we derive the conditions for oscillon solutions and explore multifield oscillon configurations. In these configurations, the two fields form colocated oscillons that oscillate with frequencies set by their respective masses. These multifield oscillons can be viewed as a bound state of two oscillons due to attractive interactions between the fields. We confirm these analytical predictions through numerical lattice calculations. This work extends the standard picture of single-field oscillons and may be relevant for cosmological scenarios involving multiple interacting real scalar fields.

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References (50)

  1. I. L. Bogolyubsky and V. G. Makhankov, Lifetime of pulsating solitons in some classical models, Pis’ma Zh. Eksp. Teor. Fiz. 24, 15 (1976), https://inspirehep.net/literature/114626.
  2. M. Gleiser, Pseudostable bubbles, Phys. Rev. D 49, 2978 (1994).
  3. E. J. Copeland, M. Gleiser, and H. R. Muller, Oscillons: Resonant configurations during bubble collapse, Phys. Rev. D 52, 1920 (1995).
  4. S. Kasuya, M. Kawasaki, and F. Takahashi, I-balls, Phys. Lett. B 559, 99 (2003).
  5. S. R. Coleman, Q-balls, Nucl. Phys. B262, 263 (1985).
  6. K. Mukaida and M. Takimoto, Correspondence of I- and Q-balls as non-relativistic condensates, J. Cosmol. Astropart. Phys. 08 (2014) 051.
  7. M. Kawasaki, F. Takahashi, and N. Takeda, Adiabatic invariance of oscillons/I-balls, Phys. Rev. D 92, 105024 (2015).
  8. M. A. Amin, R. Easther, H. Finkel, R. Flauger, and M. P. Hertzberg, Oscillons after inflation, Phys. Rev. Lett. 108, 241302 (2012).
  9. K. D. Lozanov and M. A. Amin, Self-resonance after inflation: Oscillons, transients and radiation domination, Phys. Rev. D 97, 023533 (2018).
  10. T. Hiramatsu, E. I. Sfakianakis, and M. Yamaguchi, Gravitational wave spectra from oscillon formation after inflation, J. High Energy Phys. 03 (2021) 021.
  11. M. Kawasaki, W. Nakano, and E. Sonomoto, Oscillon of ultra-light axion-like particle, J. Cosmol. Astropart. Phys. 01 (2020) 047.
  12. J. Ollé, O. Pujolàs, and F. Rompineve, Oscillons and dark matter, J. Cosmol. Astropart. Phys. 02 (2020) 006.
  13. A. Vaquero, J. Redondo, and J. Stadler, Early seeds of axion miniclusters, J. Cosmol. Astropart. Phys. 04 (2019) 012.
  14. M. Kawasaki, W. Nakano, H. Nakatsuka, and E. Sonomoto, Oscillons of axion-like particle: Mass distribution and power spectrum, J. Cosmol. Astropart. Phys. 01 (2021) 061.
  15. M. Kawasaki, W. Nakano, H. Nakatsuka, and E. Sonomoto, Probing oscillons of ultra-light axion-like particle by 21 cm forest, J. Cosmol. Astropart. Phys. 04 (2021) 019.
  16. D. Cyncynates, T. Giurgica-Tiron, O. Simon, and J. O. Thompson, Resonant nonlinear pairs in the axiverse and their late-time direct and astrophysical signatures, Phys. Rev. D 105, 055005 (2022).
  17. M. Kawasaki, K. Miyazaki, K. Murai, H. Nakatsuka, and E. Sonomoto, Anisotropies in cosmological 21 cm background by oscillons/I-balls of ultra-light axion-like particle, J. Cosmol. Astropart. Phys. 08 (2022) 066.
  18. D. Cyncynates, O. Simon, J. O. Thompson, and Z. J. Weiner, Nonperturbative structure in coupled axion sectors and implications for direct detection, Phys. Rev. D 106, 083503 (2022).
  19. M. Gleiser and D. Sicilia, Analytical characterization of oscillon energy and lifetime, Phys. Rev. Lett. 101, 011602 (2008).
  20. G. Fodor, P. Forgacs, Z. Horvath, and M. Mezei, Computation of the radiation amplitude of oscillons, Phys. Rev. D 79, 065002 (2009).
  21. M. P. Hertzberg, Quantum radiation of oscillons, Phys. Rev. D 82, 045022 (2010).
  22. P. Salmi and M. Hindmarsh, Radiation and relaxation of oscillons, Phys. Rev. D 85, 085033 (2012).
  23. K. Mukaida, M. Takimoto, and M. Yamada, On longevity of I-ball/oscillon, J. High Energy Phys. 03 (2017) 122.
  24. M. Ibe, M. Kawasaki, W. Nakano, and E. Sonomoto, Decay of I-ball/oscillon in classical field theory, J. High Energy Phys. 04 (2019) 030.
  25. M. Ibe, M. Kawasaki, W. Nakano, and E. Sonomoto, Fragileness of exact I-ball/oscillon, Phys. Rev. D 100, 125021 (2019).
  26. H.-Y. Zhang, M. A. Amin, E. J. Copeland, P. M. Saffin, and K. D. Lozanov, Classical decay rates of oscillons, J. Cosmol. Astropart. Phys. 07 (2020) 055.
  27. D. Cyncynates and T. Giurgica-Tiron, Structure of the oscillon: The dynamics of attractive self-interaction, Phys. Rev. D 103, 116011 (2021).
  28. K. Imagawa, M. Kawasaki, K. Murai, H. Nakatsuka, and E. Sonomoto, Free streaming length of axion-like particle after oscillon/I-ball decays, J. Cosmol. Astropart. Phys. 02 (2023) 024.
  29. K. Nakayama, F. Takahashi, and M. Yamada, Quantum decay of scalar and vector boson stars and oscillons into gravitons, J. Cosmol. Astropart. Phys. 08 (2023) 058.
  30. R. Friedberg, T. D. Lee, and A. Sirlin, A class of scalar-field soliton solutions in three space dimensions, Phys. Rev. D 13, 2739 (1976).
  31. J. Heeck and M. Sokhashvili, Revisiting the Friedberg–Lee–Sirlin soliton model, Eur. Phys. J. C 83, 526 (2023).
  32. E. Kim and E. Nugaev, Effectively flat potential in the Friedberg-Lee-Sirlin model, Eur. Phys. J. C 84, 797 (2024).
  33. E. Kim, E. Nugaev, and Y. Shnir, Large solitons flattened by small quantum corrections, Phys. Lett. B 856, 138881 (2024).
  34. Y. Hamada, K. Kawana, T. Kim, and P. Lu, Q-balls in the presence of attractive force, J. High Energy Phys. 08 (2024) 242.
  35. V. Jaramillo and S.-Y. Zhou, Dipoles and chains of solitons in the Friedberg-Lee-Sirlin model, Phys. Rev. D 111, 024027 (2025).
  36. M. Gleiser, N. Graham, and N. Stamatopoulos, Generation of coherent structures after cosmic inflation, Phys. Rev. D 83, 096010 (2011).
  37. S. H. Hawley and M. W. Choptuik, Numerical evidence for ‘multi-scalar stars’, Phys. Rev. D 67, 024010 (2003).
  38. R. A. C. Correa, A. de Souza Dutra, T. Frederico, B. A. Malomed, O. Oliveira, and N. Sawado, Creating oscillons and oscillating kinks in two scalar field theories, Chaos 29, 103124 (2019).
  39. F. Van Dissel and E. I. Sfakianakis, Symmetric multifield oscillons, Phys. Rev. D 106, 096018 (2022).
  40. V. Achilleos, F. K. Diakonos, D. J. Frantzeskakis, G. C. Katsimiga, X. N. Maintas, E. Manousakis et al., Oscillons and oscillating kinks in the Abelian-Higgs model, Phys. Rev. D 88, 045015 (2013).
  41. F. K. Diakonos, G. C. Katsimiga, X. N. Maintas, and C. E. Tsagkarakis, Symmetric solitonic excitations of the (1+1)-dimensional Abelian-Higgs classical vacuum, Phys. Rev. E 91, 023202 (2015).
  42. M. Kawasaki and M. Yamada, Decay rates of Gaussian-type I-balls and Bose-enhancement effects in 3+1 dimensions, J. Cosmol. Astropart. Phys. 02 (2014) 001.
  43. S. Antusch and S. Orani, Impact of other scalar fields on oscillons after hilltop inflation, J. Cosmol. Astropart. Phys. 03 (2016) 026.
  44. M. Shafi, E. J. Copeland, R. Mahbub, S. S. Mishra, and S. Basak, Formation and decay of oscillons after inflation in the presence of an external coupling: Part I. Lattice simulations, J. Cosmol. Astropart. Phys. 10 (2024) 082.
  45. S. Li, M. Yamaguchi, and Y.-l. Zhang, Decay and lifetime of oscillons coupled to an external scalar field: Insights from instability band analysis, J. Cosmol. Astropart. Phys. 12 (2025) 028.
  46. J. McDonald, Inflaton condensate fragmentation in hybrid inflation models, Phys. Rev. D 66, 043525 (2002).
  47. E. J. Copeland, S. Pascoli, and A. Rajantie, Dynamics of tachyonic preheating after hybrid inflation, Phys. Rev. D 65, 103517 (2002).
  48. M. Broadhead and J. McDonald, Simulations of the end of supersymmetric hybrid inflation and non-topological soliton formation, Phys. Rev. D 72, 043519 (2005).
  49. S. Kichenassamy, Breather solutions of the nonlinear wave equation, Commun. Pure Appl. Math. 44, 789 (1991).
  50. G. Fodor, P. Forgacs, Z. Horvath, and A. Lukacs, Small amplitude quasi-breathers and oscillons, Phys. Rev. D 78, 025003 (2008).

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Phys. Rev. D 114, 036019– Published 17 August, 2026
  • Received 16 April 2026
  • Accepted 6 July 2026
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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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