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Tachyonic and parametric resonances for massive particle production in an intense scalar plane wave background

Ekaterina Dmitrieva* and Petr Satunin†

  • *Contact author: edmitrieva@inr.ru
  • †Contact author: satunin@ms2.inr.ac.ru
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Phys. Rev. D 111, 115032 – Published 26 June, 2025

DOI: https://doi.org/10.1103/8g2f-kgml

Abstract

We investigate the stability of an intensive plane wave of a massless or light scalar field ϕ in a trilinear scalar model gϕχ2 due to the resonant production of massive χ particles in a perturbatively forbidden regime. We apply two methods. First, we solve the Heisenberg equation for the quantum amplitudes of the field χ in an external plane wave background, generalizing the solution of Arza [A. Arza, Production of massive bosons from the decay of a massless particle beam, Phys. Rev. D 105, 036004 (2022).]. Second, for the light but massive ϕ, we perform the relativistic boost to the rest frame of ϕ, reducing the problem to the stability of the thoroughly investigated massive condensate. It turns out that the stability properties are significantly different for the cases of massless and light fields. In the first case, one should adopt the Heisenberg equation approach, since the alternative method cannot provide a comprehensive outcome. In the second case, the use of the Mathieu equation provides a more accurate solution, while for the massless case, this approach is not applicable.

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References (40)

  1. V. Ritus and A. Nikishov, Quantum electrodynamics phenomena in the intense field, Trudy FIAN 111 (1979), https://proceedings.lebedev.ru/0111-1979/.
  2. W. Dittrich and H. Gies, Springer Tracts in Modern Physics, Vol. 166 (Springer, Berlin, Heidelberg, 2000).
  3. A. Kuznetsov and N. Mikheev, Springer Tracts in Modern Physics, Vol. 252 (Springer, New York, 2013).
  4. E. A. Calzetta and B.-L. B. Hu, Nonequilibrium Quantum Field Theory, Cambridge Monographs on Mathematical Physics (Cambridge University Press, Cambridge, England, 2023).
  5. A. Fedotov, A. Ilderton, F. Karbstein, B. King, D. Seipt, H. Taya, and G. Torgrimsson, Advances in QED with intense background fields, Phys. Rep. 1010, 1 (2023).
  6. A. A. Grib, S. G. Mamaev, and V. Mostepanenko, Vacuum Quantum Effects in Strong Fields (Friedmann Laboratory Pub., 1994).
  7. A. A. Grib, S. G. Mamayev, and V. M. Mostepanenko, Vacuum Quantum Effects in Strong Fields (Friedmann Laboratory Publishing, St. Petersburg, 1994).
  8. L. Kofman, A. D. Linde, and A. A. Starobinsky, Towards the theory of reheating after inflation, Phys. Rev. D 56, 3258 (1997).
  9. K. Lozanov, Reheating After Inflation (Springer, New York, 2020).
  10. J. F. Dufaux, G. N. Felder, L. Kofman, M. Peloso, and D. Podolsky, Preheating with trilinear interactions: Tachyonic resonance, J. Cosmol. Astropart. Phys. 07 (2006) 006.
  11. C. Eröncel, Axion-like-particle dark matter beyond the standard paradigm, arXiv:2501.11717.
  12. R. Wiley Deal, L. Barrowes, J. T. Giblin, K. Sinha, S. Watson, and F. C. Adams, Cosmological moduli and non-perturbative production of axions, arXiv:2501.17229.
  13. L. Kofman, A. D. Linde, and A. A. Starobinsky, Reheating after inflation, Phys. Rev. Lett. 73, 3195 (1994).
  14. J. H. Traschen and R. H. Brandenberger, Particle production during out-of-equilibrium phase transitions, Phys. Rev. D 42, 2491 (1990).
  15. Y. Shtanov, J. H. Traschen, and R. H. Brandenberger, Universe reheating after inflation, Phys. Rev. D 51, 5438 (1995).
  16. S. Y. Khlebnikov and I. I. Tkachev, Classical decay of inflaton, Phys. Rev. Lett. 77, 219 (1996).
  17. S. Y. Khlebnikov and I. I. Tkachev, The Universe after inflation: The wide resonance case, Phys. Lett. B 390, 80 (1997).
  18. R. Allahverdi, R. Brandenberger, F.-Y. Cyr-Racine, and A. Mazumdar, Reheating in inflationary cosmology: Theory and applications, Annu. Rev. Nucl. Part. Sci. 60, 27 (2010).
  19. M. A. Amin, M. P. Hertzberg, D. I. Kaiser, and J. Karouby, Nonperturbative dynamics of reheating after inflation: A review, Int. J. Mod. Phys. D 24, 1530003 (2014).
  20. N. W. McLachlan, Theory and Application of Mathieu Functions (Clarendon Press, Oxford, 1947).
  21. R. N. Jazar, Perturbation Methods in Science and Engineering (Springer, New York, 2021).
  22. K. Schmitz and G. Vertongen, Reheating and preheating after inflation: An introduction, Reh 6, t2 (2010), https://www.desy.de/~westphal/workshop_seminar_fall_2010/reheating.pdf.
  23. H. Fujisaki, K. Kumekawa, M. Yoshimura, and M. Yamaguchi, Particle production and gravitino abundance after inflation, Phys. Rev. D 54, 2494 (1996).
  24. M. Abramowitz and I. Stegun, Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables, Applied Mathematics Series (Dover Publications, New York, 1965).
  25. A. Y. Andreev and D. A. Kirzhnits, Tachyons and the instability of physical systems, Phys. Usp. 39, 1071 (1996).
  26. G. Feinberg, Possibility of faster-than-light particles, Phys. Rev. 159, 1089 (1967).
  27. S. Khlebnikov and I. Tkachev, Resonant decay of cosmological Bose condensates, Phys. Rev. Lett. 79, 1607 (1997).
  28. D. G. Levkov, A. G. Panin, and I. I. Tkachev, Radio-emission of axion stars, Phys. Rev. D 102, 023501 (2020).
  29. K. A. Beyer, G. Marocco, C. Danson, R. Bingham, and G. Gregori, Parametric co-linear axion photon instability, Phys. Lett. B 839, 137759 (2023).
  30. C. Cronström and M. Noga, Photon induced relativistic band structure in dielectrics, Phys. Lett. 60A, 137 (1977).
  31. W. Becker, Relativistic charged particles in the field of an electromagnetic plane wave in a medium, Physica A (Amsterdam) 87, 601 (1977).
  32. T. Heinzl, A. Ilderton, and B. King, Classical and quantum particle dynamics in univariate background fields, Phys. Rev. D 94, 065039 (2016).
  33. B. King and H. Hu, Classical and quantum dynamics of a charged scalar particle in a background of two counterpropagating plane waves, Phys. Rev. D 94, 125010 (2016).
  34. A. Arza, Production of massive bosons from the decay of a massless particle beam, Phys. Rev. D 105, 036004 (2022).
  35. J. T. Mendonça and A. Serbeto, Volkov solutions for relativistic quantum plasmas, Phys. Rev. E 83, 026406 (2011).
  36. E. Raicher, S. Eliezer, and A. Zigler, Nonlinear Compton scattering in a strong rotating electric field, Phys. Rev. A 94, 062105 (2016).
  37. L. D. Landau and E. Lifshitz, Mechanics: Volume 1 (Butterworth-Heinemann, 1982).
  38. R. Allahverdi, R. H. A. D. Shaw, and B. A. Campbell, Parametric resonance for complex fields, Phys. Lett. B 473, 246 (2000).
  39. E. Dmitrieva and P. Satunin, The effects of the birth of particles in the field of waves of high intensity, Proc. Sci. ICPPCRubakov2023 (2024) 047.
  40. L. D. Landau and E. Lifshitz, The Classical Theory of Fields: Volume 2 Course of theoretical physics (Elsevier Science, 1975).

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Phys. Rev. D 111, 115032– Published 26 June, 2025
  • Received 14 April 2025
  • Accepted 5 June 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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