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Misalignment dynamics of scalar condensates with Yukawa coupling: Particle and entropy production

Nathan Herring1,* and Daniel Boyanovsky2,†

  • *Contact author: nherring@hillsdale.edu
  • †Contact author: boyan@pitt.edu
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Phys. Rev. D 113, 043503 – Published 5 February, 2026

DOI: https://doi.org/10.1103/hrhp-kcwj

Abstract

Misalignment dynamics, the nonequilibrium evolution of a scalar (or pseudoscalar) condensate in a potential landscape, broadly describes a solution to the strong CP problem, a mechanism for cold dark matter production and (pre)reheating postinflation. Often, when radiative corrections are included phenomenologically by replacing the potential by the effective potential which is a static quantity, its usefulness is restricted to (near) equilibrium situations. We study the misalignment dynamics of a scalar condensate Yukawa coupled to Nf fermions in a manifestly energy conserving, fully renormalized Hamiltonian framework. A large Nf limit allows us to focus on the fermion degrees of freedom, which yield a negative contribution to the effective potential, a radiatively induced instability and ultraviolet divergent field renormalization. We introduce an adiabatic basis and an adiabatic expansion that embodies the derivative expansion in the effective action, the zeroth order is identified with the effective potential, higher orders account for the derivative expansion including field renormalization, and describe profuse particle production. Energy conserving dynamics leads to the conjecture of emergent asymptotic highly excited stationary states with a distribution function nk(∞)∝1/k6 and an extensive entropy which is identified with an entanglement entropy. Subtle aspects of renormalization associated with the initial value problem are analyzed and resolved. Possible new manifestations of asymptotic spontaneous symmetry breaking (SSB) as a consequence of the dynamics, even in the absence of tree-level SSB, and cosmological inferences are discussed.

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References (51)

  1. R. D. Peccei and H. R. Quinn, Phys. Rev. Lett. 38, 1440 (1977).
  2. R. D. Peccei and H. R. Quinn, Phys. Rev. D 16, 1791 (1977).
  3. J. Preskill, M. B. Wise, and F. Wilczek, Phys. Lett. 120B, 127 (1983).
  4. L. F. Abbott and P. Sikivie, Phys. Lett. 120B, 133 (1983).
  5. M. Dine and W. Fischler, Phys. Lett. 120B, 137 (1983).
  6. G. Jona-Lasinio, Nuovo Cimento 34, 1790 (1964).
  7. J. Goldstone, A. Salam, and S. Weinberg, Phys. Rev. 127, 965 (1962).
  8. S. Coleman and E. Weinberg, Phys. Rev. D 7, 1888 (1973).
  9. S. Coleman, Aspects of Symmetry (Cambridge University Press, NY, 1985).
  10. R. Jackiw, Phys. Rev. D 9, 1686 (1974).
  11. J. Iliopoulos, C. Itzykson, and A. Martin, Rev. Mod. Phys. 47, 165 (1975).
  12. S. Coleman, R. Jackiw, and H. D. Politzer, Phys. Rev. D 10, 2491 (1974).
  13. L. Dolan and R. Jackiw, Phys. Rev. D 9, 3320 (1974).
  14. S. Weinberg, Phys. Rev. D 9, 3357 (1974).
  15. R. H. Brandenberger, Rev. Mod. Phys. 57, 1 (1985).
  16. N. Herring, S. Cao, and D. Boyanovsky, Phys. Rev. D 109, 105021 (2024); 111, 016028 (2025).
  17. L. Kofman, A. Linde, and A. Starobinsky, Phys. Rev. Lett. 73, 3195 (1994); Phys. Rev. D 56, 3258 (1997).
  18. Y. Shtanov, J. Trashen, and R. Brandenberger, Phys. Rev. D 51, 5438 (1995).
  19. L. Kofman, arXiv:astro-ph/9605155; arXiv:hep-ph/9802285; L. Kofman and P. Yi, Phys. Rev. D 72, 106001 (2005); L. Kofman, arXiv:astro-ph/9605155.
  20. R. H. Brandenberger, arXiv:hep-ph/9701276.
  21. R. Allahverdi, R. Brandenberger, F.-Y. Cyr-Racine, and A. Mazumdar, Annu. Rev. Nucl. Part. Sci. 60, 27 (2010).
  22. F. Finelli and R. Brandenberger, Phys. Rev. D 62, 083502 (2000); Phys. Rev. Lett. 82, 1362 (1999).
  23. M. A. Amin, M. P. Hertzberg, D. I. Kaiser, and J. Karouby, Int. J. Mod. Phys. D 24, 1530003 (2015); D. Kaiser, Phys. Rev. D 53, 1776 (1996).
  24. N. Barnaby, J. Braden, and L. Kofman, J. Cosmol. Astropart. Phys. 07 (2010) 016.
  25. P. B. Greene and L. Kofman, Phys. Lett. B 448, 6 (1999); Phys. Rev. D 62, 123516 (2000).
  26. M. Peloso and L. Sorbo, J. High Energy Phys. 05 (2000) 016.
  27. S. Tsujikawa, B. A. Bassett, and F. Viniegra, J. High Energy Phys. 08 (2000) 019.
  28. J. Garcia-Bellido, S. Mollerach, and E. Roulet, J. High Energy Phys. 02 (2000) 034.
  29. J. Berges, D. Gelfand, and J. Pruschke, Phys. Rev. Lett. 107, 061301 (2011).
  30. M. Sher, Phys. Rep. 179, 273 (1989); Phys. Lett B 317, 159 (1993); Phys. Rev. D 54, 7071 (1996).
  31. M. Lindner, M. Sher, and H. W. Zaglauer, Phys. Lett. B 228, 139 (1989).
  32. S. Nie and M. Sher, Phys. Lett. 449B, 89 (1999).
  33. K. Symanzik, Commun. Math. Phys. 16, 48 (1970).
  34. E. J. Weinberg and A. Wu, Phys. Rev. D 36, 2474 (1987).
  35. J. Baacke, K. Heitmann, and C. Patzold, Phys. Rev. D 58, 125013 (1998); J. Baacke and C. Patzold, 62, 084008 (2000).
  36. F. Cooper and E. Mottola, Mod. Phys. Lett. A 02, 635 (1987); Phys. Rev. D 36, 3114 (1987); 40, 456 (1989).
  37. J. Baacke, K. Heitmann, and C. Patzold, Phys. Rev. D 57, 6398 (1998).
  38. J. Baacke, D. Boyanovsky, and H. J. de Vega, Phys. Rev. D 63, 045023 (2001).
  39. D. Boyanovsky, H. J. de Vega, R. Holman, and M. R. Martin, Phys. Rev. D 65, 045007 (2002).
  40. G. V. Dunne, arXiv:2511.15528.
  41. M. Srednicki, Phys. Rev. E 50, 888 (1994); J. Phys. A 32, 1163 (1999).
  42. M. Rigol, V. Dunjko, and M. Olshanii, Nature (London) 452, 854 (2008).
  43. J. M. Deutsch,Phys. Rev. A 43, 2046 (1991); Rep. Prog. Phys. 81, 082001 (2018).
  44. S.-Y. Lin, C.-H. Chou, and B. L. Hu, Phys. Rev. D 81, 084018 (2010); B. L. Hu and D. Pavon, Phys. Lett. B 180, 329 (1986); D. Koks, A. Matacz, and B. L. Hu, Phys. Rev. D 55, 5917 (1997).
  45. W. H. Zurek, Phys. Rev. D 24, 1516 (1981).
  46. J. R. Anglin and W. H. Zurek, Phys. Rev. D 53, 7327 (1996).
  47. J. M. Cornwall, R. Jackiw, and E. Tomboulis, Phys. Rev. D 10, 2428 (1974).
  48. J. Berges and B. Wallisch, Phys. Rev. D 95, 036016 (2017); J. Berges, arXiv:1503.02907; J. Berges, A. Rothkopf, and J. Schmidt, Phys. Rev. Lett. 101, 041603 (2008); J. Berges and Sz. Borsanyi, Nucl. Phys. A785, 58 (2007); J. Berges, AIP Conf. Proc. 739, 3 (2004); J. Berges and J. Serreau, Phys. Rev. Lett. 91, 111601 (2003).
  49. A. Giraud and J. Serreau, Phys. Rev. Lett. 104, 230405 (2010).
  50. N. Herring, D. Boyanovsky, and A. Zentner, Phys. Rev. D 101, 083516 (2020); N. Herring and D. Boyanovsky, 101, 123522 (2020).
  51. G. V. Dunne and T. M. Hall, Phys. Rev. D 60, 065002 (1999).

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Phys. Rev. D 113, 043503– Published 5 February, 2026
  • Received 27 November 2025
  • Accepted 20 January 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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