- Open Access
Testing the type-II seesaw mechanism with gravitational waves
Phys. Rev. D 113, 075026 – Published 20 April, 2026
DOI: https://doi.org/10.1103/l2q2-7fjv
Abstract
Traditional seesaw mechanisms provide an elegant theoretical framework in explaining the tiny yet nonzero masses of neutrinos. Nevertheless, they face significant challenges in experimental searches, primarily because the energy scale associated with the seesaw mechanism is too high to be directly reached by terrestrial experiments. In this paper, we explore the gravitational waves (GWs) generated via graviton bremsstrahlung during the decay of seesaw particles in the early Universe. Specifically, we compute the GW spectrum resulting from the decay of the Higgs triplet within the type-II seesaw model. Our results demonstrate that the resulting GW spectrum depends sensitively on the mass of the Higgs triplet and its couplings to the Standard Model Higgs doublet and the left-handed lepton doublets. The detection of such a high-frequency GW background could offer a unique experimental window into the seesaw mechanism and provide indirect evidence for its validity.
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References (92)
- P. Minkowski, at a rate of one out of muon decays?, Phys. Lett. 67B, 421 (1977).
- T. Yanagida, Horizontal gauge symmetry and masses of neutrinos, Conf. Proc. C 7902131, 95 (1979).
- M. Gell-Mann, P. Ramond, and R. Slansky, Complex spinors and unified theories, Conf. Proc. C 790927, 315 (1979).
- S. L. Glashow, The future of elementary particle physics, NATO Sci. Ser. B 61, 687 (1980).
- R. N. Mohapatra and G. Senjanovic, Neutrino mass and spontaneous parity nonconservation, Phys. Rev. Lett. 44, 912 (1980).
- M. Fukugita and T. Yanagida, Baryogenesis without grand unification, Phys. Lett. B 174, 45 (1986).
- Y. Cai, J. Herrero-García, M. A. Schmidt, A. Vicente, and R. R. Volkas, From the trees to the forest: A review of radiative neutrino mass models, Front. Phys. 5, 63 (2017).
- A. Zee, A theory of lepton number violation, neutrino Majorana mass, and oscillation, Phys. Lett. 93B, 389 (1980); 95B, 461(E) (1980).
- K. S. Babu, Model of “calculable” Majorana neutrino masses, Phys. Lett. B 203, 132 (1988).
- E. Ma, Verifiable radiative seesaw mechanism of neutrino mass and dark matter, Phys. Rev. D 73, 077301 (2006).
- W. Chao, Neutrino masses and a TeV scale seesaw mechanism, Phys. Rev. D 82, 016008 (2010).
- M. Lindner, M. Platscher, and F. S. Queiroz, A call for new physics: The muon anomalous magnetic moment and lepton flavor violation, Phys. Rep. 731, 1 (2018).
- W. Rodejohann, Neutrino-less double beta decay and particle physics, Int. J. Mod. Phys. E 20, 1833 (2011).
- Y. Cui and Z.-Z. Xianyu, Probing leptogenesis with the cosmological collider, Phys. Rev. Lett. 129, 111301 (2022).
- B. P. Abbott et al., Observation of gravitational waves from a binary black hole merger, Phys. Rev. Lett. 116, 061102 (2016).
- B. Barman, N. Bernal, Y. Xu, and Ó. Zapata, Gravitational wave from graviton bremsstrahlung during reheating, J. Cosmol. Astropart. Phys. 05 (2023) 019.
- X.-J. Xu, Y. Xu, Q. Yin, and J. Zhu, Full-spectrum analysis of gravitational wave production from inflation to reheating, J. High Energy Phys. 10 (2025) 141.
- D. Huang and L. Yin, Stochastic gravitational waves from inflaton decays, Phys. Rev. D 100, 043538 (2019).
- B. Barman, N. Bernal, Y. Xu, and Ó. Zapata, Bremsstrahlung-induced gravitational waves in monomial potentials during reheating, Phys. Rev. D 108, 083524 (2023).
- N. Bernal, S. Cléry, Y. Mambrini, and Y. Xu, Probing reheating with graviton bremsstrahlung, J. Cosmol. Astropart. Phys. 01 (2024) 065.
- Y. Xu, Ultra-high frequency gravitational waves from scattering, Bremsstrahlung and decay during reheating, J. High Energy Phys. 10 (2024) 174.
- Y. Xu, Gravitational wave from graviton Bremsstrahlung during reheating, Proc. Sci. CORFU2023 (2024) 047.
- N. Bernal and Y. Xu, Thermal gravitational waves during reheating, J. High Energy Phys. 01 (2025) 137.
- N. Bernal, Q.-f. Wu, X.-J. Xu, and Y. Xu, Pre-thermalized gravitational waves, J. High Energy Phys. 08 (2025) 125.
- A. Tokareva, Gravitational waves from inflaton decay and bremsstrahlung, Phys. Lett. B 853, 138695 (2024).
- S. Kanemura and K. Kaneta, Gravitational waves from particle decays during reheating, Phys. Lett. B 855, 138807 (2024).
- G. Montefalcone, B. Shams Es Haghi, T. Xu, and K. Freese, Thermal gravitons from warm inflation, Phys. Rev. D 112, 063556 (2025).
- Y. Ema, R. Jinno, and K. Nakayama, High-frequency graviton from inflaton oscillation, J. Cosmol. Astropart. Phys. 09 (2020) 015.
- P. Klose, M. Laine, and S. Procacci, Gravitational wave background from non-Abelian reheating after axion-like inflation, J. Cosmol. Astropart. Phys. 05 (2022) 021.
- P. Klose, M. Laine, and S. Procacci, Gravitational wave background from vacuum and thermal fluctuations during axion-like inflation, J. Cosmol. Astropart. Phys. 12 (2022) 020.
- H. An, K.-F. Lyu, L.-T. Wang, and S. Zhou, Gravitational waves from an inflation triggered first-order phase transition, J. High Energy Phys. 06 (2022) 050.
- X.-H. Hu and Y.-L. Zhou, Gravitational waves of GUT phase transition during inflation, Phys. Rev. D 111, 115003 (2025).
- W. Chao, W.-F. Cui, H.-K. Guo, and J. Shu, Gravitational wave imprint of new symmetry breaking, Chin. Phys. C 44, 123102 (2020).
- W. Chao, H.-K. Guo, and J. Shu, Gravitational wave signals of electroweak phase transition triggered by dark matter, J. Cosmol. Astropart. Phys. 09 (2017) 009.
- W. Chao, J.-j. Feng, H.-k. Guo, and T. Li, Oscillations of ultralight dark photon into gravitational waves, Nucl. Phys. B1009, 116740 (2024).
- Y. Wang and W. Chao, Gravitational wave spectrum from the production of dark matter via the freeze-in mechanism, arXiv:2508.10665.
- P. Konar and S. Show, Unraveling freeze-in dark matter through the echoes of gravitational waves, arXiv:2506.08106.
- C. Caprini, R. Durrer, and G. Servant, The stochastic gravitational wave background from turbulence and magnetic fields generated by a first-order phase transition, J. Cosmol. Astropart. Phys. 12 (2009) 024.
- M. Hindmarsh, S. J. Huber, K. Rummukainen, and D. J. Weir, Shape of the acoustic gravitational wave power spectrum from a first order phase transition, Phys. Rev. D 96, 103520 (2017); 101, 089902(E) (2020).
- P. Athron, C. Balázs, A. Fowlie, L. Morris, and L. Wu, Cosmological phase transitions: From perturbative particle physics to gravitational waves, Prog. Part. Nucl. Phys. 135, 104094 (2024).
- W. Chao, H.-K. Guo, and X.-F. Li, First order color symmetry breaking and restoration triggered by electroweak symmetry non-restoration, Phys. Lett. B 849, 138430 (2024).
- J. Ghiglieri and M. Laine, Gravitational wave background from standard model physics: Qualitative features, J. Cosmol. Astropart. Phys. 07 (2015) 022.
- A. Ringwald and C. Tamarit, Revealing the cosmic history with gravitational waves, Phys. Rev. D 106, 063027 (2022).
- J. Ghiglieri, J. Schütte-Engel, and E. Speranza, Freezing-in gravitational waves, Phys. Rev. D 109, 023538 (2024).
- J. Ghiglieri, M. Laine, J. Schütte-Engel, and E. Speranza, Double-graviton production from standard model plasma, J. Cosmol. Astropart. Phys. 04 (2024) 062.
- A. Ringwald, J. Schütte-Engel, and C. Tamarit, Gravitational waves as a big bang thermometer, J. Cosmol. Astropart. Phys. 03 (2021) 054.
- A. Datta and A. Sil, Probing leptogenesis through gravitational waves, arXiv:2410.01900.
- K.-Y. Choi, E. Lkhagvadorj, and S. Mahapatra, Cosmological origin of the KM3-230213A event and associated gravitational waves, J. Cosmol. Astropart. Phys. 10 (2025) 079.
- H. Murayama, B. Noether, and J. Schütte-Engel, Observing leptogenesis in action with gravitational waves, J. Cosmol. Astropart. Phys. 12 (2025) 027.
- S. Kanemura, K. Kaneta, and D. Nanda, Gravitational waves from supermassive right-handed neutrinos produced at preheating, Phys. Rev. D 113, 055046 (2026).
- N. Herman, A. Füzfa, L. Lehoucq, and S. Clesse, Detecting planetary-mass primordial black holes with resonant electromagnetic gravitational-wave detectors, Phys. Rev. D 104, 023524 (2021).
- N. Herman, L. Lehoucq, and A. Fúzfa, Electromagnetic antennas for the resonant detection of the stochastic gravitational wave background, Phys. Rev. D 108, 124009 (2023).
- P. Fileviez Perez, T. Han, G.-y. Huang, T. Li, and K. Wang, Neutrino masses and the CERN LHC: Testing type II seesaw, Phys. Rev. D 78, 015018 (2008).
- S. Navas et al., Review of particle physics, Phys. Rev. D 110, 030001 (2024).
- B. Pontecorvo, Mesonium and antimesonium, Sov. Phys. JETP 6, 429 (1958).
- Z. Maki, M. Nakagawa, and S. Sakata, Remarks on the unified model of elementary particles, Prog. Theor. Phys. 28, 870 (1962).
- B. Pontecorvo, Neutrino experiments and the problem of conservation of leptonic charge, Zh. Eksp. Teor. Fiz. 53, 1717 (1967).
- T. Li, C.-Y. Yao, and M. Yuan, Revealing the origin of neutrino masses through the type II seesaw mechanism at high-energy muon colliders, J. High Energy Phys. 03 (2023) 137.
- S. Ansarifard and Y. Farzan, Revisiting pseudo-Dirac neutrino scenario after recent solar neutrino data, Phys. Rev. D 107, 075029 (2023).
- I. Esteban, M. C. Gonzalez-Garcia, M. Maltoni, T. Schwetz, and A. Zhou, The fate of hints: Updated global analysis of three-flavor neutrino oscillations, J. High Energy Phys. 09 (2020) 178.
- M. M. Ivanov, J. M. Sullivan, S.-F. Chen, A. Chudaykin, M. Maus, and O. H. E. Philcox, Reanalyzing DESI DR1: 4. Percent-level cosmological constraints from combined probes and robust evidence for the normal neutrino mass hierarchy, arXiv:2601.16165.
- A. G. Adame et al., DESI 2024 VI: Cosmological constraints from the measurements of baryon acoustic oscillations, J. Cosmol. Astropart. Phys. 02 (2025) 021.
- J.-Q. Jiang, W. Giarè, S. Gariazzo, M. G. Dainotti, E. Di Valentino, O. Mena, D. Pedrotti, S. S. da Costa, and S. Vagnozzi, Neutrino cosmology after DESI: Tightest mass upper limits, preference for the normal ordering, and tension with terrestrial observations, J. Cosmol. Astropart. Phys. 01 (2025) 153.
- P. A. Zyla et al., Review of particle physics, Prog. Theor. Exp. Phys. 2020, 083C01 (2020).
- R. Zhou, L. Bian, and Y. Du, Electroweak phase transition and gravitational waves in the type-II seesaw model, J. High Energy Phys. 08 (2022) 205.
- N. D. Barrie, C. Han, and H. Murayama, Type II seesaw leptogenesis, J. High Energy Phys. 05 (2022) 160.
- E. J. Chun, K. Y. Lee, and S. C. Park, Testing Higgs triplet model and neutrino mass patterns, Phys. Lett. B 566, 142 (2003).
- D. Hooper, Particle Cosmology and Astrophysics (Princeton University Press, Princeton, NJ, 2024).
- E. W. Kolb and M. S. Turner, The Early Universe (Taylor and Francis, London, 2019), Vol. 69, 10.1201/9780429492860.
- C. Caprini et al., Science with the space-based interferometer eLISA. II: Gravitational waves from cosmological phase transitions, J. Cosmol. Astropart. Phys. 04 (2016) 001.
- C. Caprini et al., Detecting gravitational waves from cosmological phase transitions with LISA: An update, J. Cosmol. Astropart. Phys. 03 (2020) 024.
- M. B. Hindmarsh, M. Lüben, J. Lumma, and M. Pauly, Phase transitions in the early universe, SciPost Phys. Lect. Notes 24, 1 (2021).
- Y. Gouttenoire, Beyond the Standard Model Cocktail, Springer Theses (Springer, Cham, 2022), 10.1007/978-3-031-11862-3.
- G. Servant and P. Simakachorn, Ultrahigh frequency primordial gravitational waves beyond the kHz: The case of cosmic strings, Phys. Rev. D 109, 103538 (2024).
- S. Weinberg, Infrared photons and gravitons, Phys. Rev. 140, B516 (1965).
- B. R. Holstein, Graviton physics, Am. J. Phys. 74, 1002 (2006).
- A. Berlin, D. Blas, R. T. D’Agnolo, S. A. Ellis, R. Harnik, Y. Kahn, and J. Schütte-Engel, Detecting high-frequency gravitational waves with microwave cavities, Phys. Rev. D 105, 116011 (2022).
- A. Berlin, D. Blas, R. T. d’Agnolo, S. A. Ellis, R. Harnik, Y. Kahn, J. Schütte-Engel, and M. Wentzel, Electromagnetic cavities as mechanical bars for gravitational waves, Phys. Rev. D 108, 084058 (2023).
- R. Capdevilla, G. B. Gelmini, J. Hyman, A. J. Millar, and E. Vitagliano, Gravitational wave detection with plasma haloscopes, Phys. Rev. D 112, 055011 (2025).
- J. Chluba et al., New horizons in cosmology with spectral distortions of the cosmic microwave background, Exp. Astron. 51, 1515 (2021).
- A. Kogut, D. Fixsen, D. Chuss, J. Dotson, E. Dwek, M. Halpern, G. Hinshaw, S. Meyer, S. Moseley, M. Seiffert et al., The primordial inflation explorer (pixie): A nulling polarimeter for cosmic microwave background observations, J. Cosmol. Astropart. Phys. 07 (2011) 025.
- A. Kogut, M. H. Abitbol, J. Chluba, J. Delabrouille, D. Fixsen, J. C. Hill, S. P. Patil, and A. Rotti, CMB spectral distortions: Status and prospects, Bull. Am. Astron. Soc. 51, 113 (2019).
- K. Basu et al., A space mission to map the entire observable universe using the CMB as a backlight: Voyage 2050 science white paper, Exp. Astron. 51, 1555 (2021).
- E. Ma and U. Sarkar, Neutrino masses and leptogenesis with heavy Higgs triplets, Phys. Rev. Lett. 80, 5716 (1998).
- K. Nakayama and Y. Tang, Stochastic gravitational waves from particle origin, Phys. Lett. B 788, 341 (2019); 839, 137787(E) (2023).
- P. de Aquino, K. Hagiwara, Q. Li, and F. Maltoni, Simulating graviton production at hadron colliders, J. High Energy Phys. 06 (2011) 132.
- D. J. Gross and R. Jackiw, Low-energy theorem for graviton scattering, Phys. Rev. 166, 1287 (1968).
- T. Gleisberg, F. Krauss, K. T. Matchev, A. Schalicke, S. Schumann, and G. Soff, Helicity formalism for spin-2 particles, J. High Energy Phys. 09 (2003) 001.
- R. Mertig, M. Böhm, and A. Denner, Feyn calc-computer-algebraic calculation of feynman amplitudes, Comput. Phys. Commun. 64, 345 (1991).
- V. Shtabovenko, R. Mertig, and F. Orellana, New developments in feyncalc 9.0, Comput. Phys. Commun. 207, 432 (2016).
- V. Shtabovenko, R. Mertig, and F. Orellana, feyncalc 9.3: New features and improvements, Comput. Phys. Commun. 256, 107478 (2020).
- V. Shtabovenko, R. Mertig, and F. Orellana, feyncalc 10: Do multiloop integrals dream of computer codes?, Comput. Phys. Commun. 306, 109357 (2025).