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Neutrino masses, matter-antimatter asymmetry, dark matter, and supermassive black hole formation explained with Majorons

Yifan Lu1,*, Zachary S. C. Picker1,†, Alexander Kusenko1,2,‡, and Tsutomu T. Yanagida2,3,§

  • *Contact author: yifanlu@ucla.edu
  • †Contact author: zpicker@physics.ucla.edu
  • ‡Contact author: kusenko@ucla.edu
  • §Contact author: tsutomu.tyanagida@sjtu.edu.cn
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Phys. Rev. D 113, 015037 – Published 23 January, 2026

DOI: https://doi.org/10.1103/4gy4-8c32

Abstract

The spontaneous breaking of a global lepton number symmetry can result in a (pseudo) Nambu-Goldstone boson known as the Majoron. We study a singlet Majoron model that couples to two Higgs doublets in which the lepton number current develops an electromagnetic anomaly, allowing the decay of Majorons into photons. We focus on Majorons at the eV scale with an enhanced anomaly and show that it serves as a dark matter candidate whose decay signals can be probed by space telescope observations. Furthermore, if the decay produces Lyman-Werner photons, heavy black hole seeds can be generated via the direct collapse mechanism and evolve into the active galactic nuclei we observe at high redshifts. Our framework thus simultaneously addresses the origin of neutrino masses, the baryon asymmetry of the Universe, the nature of dark matter, and the formation of high redshift supermassive black holes.

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References (106)

  1. P. Minkowski, μ→eγ at a rate of one out of 109 muon decays?, Phys. Lett. 67B, 421 (1977).
  2. T. Yanagida, Horizontal gauge symmetry and masses of neutrinos, Conf. Proc. C 7902131, 95 (1979).
  3. T. Yanagida, Horizontal symmetry and mass of the top quark, Phys. Rev. D 20, 2986 (1979).
  4. S. L. Glashow, The future of elementary particle physics, NATO Sci. Ser. B 61, 687 (1980).
  5. M. Gell-Mann, P. Ramond, and R. Slansky, Complex spinors and unified theories, Conf. Proc. C 790927, 315 (1979).
  6. M. Fukugita and T. Yanagida, Baryogenesis without grand unification, Phys. Lett. B 174, 45 (1986).
  7. W. Buchmuller, R. D. Peccei, and T. Yanagida, Leptogenesis as the origin of matter, Annu. Rev. Nucl. Part. Sci. 55, 311 (2005).
  8. V. A. Kuzmin, V. A. Rubakov, and M. E. Shaposhnikov, On the anomalous electroweak baryon number nonconservation in the early universe, Phys. Lett. 155B, 36 (1985).
  9. Y. Chikashige, R. N. Mohapatra, and R. D. Peccei, Spontaneously broken lepton number and cosmological constraints on the neutrino mass spectrum, Phys. Rev. Lett. 45, 1926 (1980).
  10. Y. Chikashige, R. N. Mohapatra, and R. D. Peccei, Are there real goldstone bosons associated with broken lepton number?, Phys. Lett. 98B, 265 (1981).
  11. G. B. Gelmini and M. Roncadelli, Left-handed neutrino mass scale and spontaneously broken lepton number, Phys. Lett. 99B, 411 (1981).
  12. I. Z. Rothstein, K. S. Babu, and D. Seckel, Planck scale symmetry breaking and Majoron physics, Nucl. Phys. B403, 725 (1993).
  13. P. Langacker, R. D. Peccei, and T. Yanagida, Invisible axions and light neutrinos: Are they connected?, Mod. Phys. Lett. A 01, 541 (1986).
  14. M. Lattanzi and J. W. F. Valle, Decaying warm dark matter and neutrino masses, Phys. Rev. Lett. 99, 121301 (2007).
  15. P.-H. Gu, E. Ma, and U. Sarkar, Pseudo-Majoron as dark matter, Phys. Lett. B 690, 145 (2010).
  16. M. Frigerio, T. Hambye, and E. Masso, Sub-GeV dark matter as pseudo-Goldstone from the seesaw scale, Phys. Rev. X 1, 021026 (2011).
  17. W. Wang and Z.-L. Han, Global U(1)L breaking in neutrinophilic 2HDM: From LHC signatures to x-ray line, Phys. Rev. D 94, 053015 (2016).
  18. Y. Abe, Y. Hamada, T. Ohata, K. Suzuki, and K. Yoshioka, TeV-scale Majorogenesis, J. High Energy Phys. 07 (2020) 105.
  19. S. K. Manna and A. Sil, Majorons revisited: Light dark matter as a FIMP, Phys. Rev. D 108, 075026 (2023).
  20. V. Berezinsky and J. W. F. Valle, The KeV Majoron as a dark matter particle, Phys. Lett. B 318, 360 (1993).
  21. F. Bazzocchi, M. Lattanzi, S. Riemer-Sørensen, and J. W. F. Valle, X-ray photons from late-decaying Majoron dark matter, J. Cosmol. Astropart. Phys. 08 (2008) 013.
  22. F. S. Queiroz and K. Sinha, The poker face of the Majoron dark matter model: LUX to keV line, Phys. Lett. B 735, 69 (2014).
  23. E. Dudas, Y. Mambrini, and K. A. Olive, Monochromatic neutrinos generated by dark matter and the seesaw mechanism, Phys. Rev. D 91, 075001 (2015).
  24. C. Garcia-Cely and J. Heeck, Neutrino lines from Majoron dark matter, J. High Energy Phys. 05 (2017) 102.
  25. A. Greljo, X. Ponce Díaz, and A. E. Thomsen, Insights on the cosmic origin of matter from proton stability, J. Cosmol. Astropart. Phys. 11 (2025) 043.
  26. M. Lattanzi, S. Riemer-Sorensen, M. Tortola, and J. W. F. Valle, Updated CMB and x- and γ-ray constraints on Majoron dark matter, Phys. Rev. D 88, 063528 (2013).
  27. K. Akita and M. Niibo, Updated constraints and future prospects on Majoron dark matter, J. High Energy Phys. 07 (2023) 132.
  28. Q. Liang, X. Ponce Díaz, and T. T. Yanagida, Axion detection experiments can probe Majoron models, Phys. Rev. Lett. 134, 151803 (2025).
  29. E. Todarello, M. Regis, J. Reynoso-Cordova, M. Taoso, D. Vaz, J. Brinchmann, M. Steinmetz, and S. L. Zoutendijk, Robust bounds on ALP dark matter from dwarf spheroidal galaxies in the optical MUSE-Faint survey, J. Cosmol. Astropart. Phys. 05 (2024) 043.
  30. E. Todarello and M. Regis, Bounds on axions-like particles shining in the ultra-violet, J. Cosmol. Astropart. Phys. 05 (2025) 070.
  31. E. Pinetti, First constraints on QCD axion dark matter using James Webb Space Telescope observations, arXiv:2503.11753.
  32. P. Carenza, G. Lucente, and E. Vitagliano, Probing the blue axion with cosmic optical background anisotropies, Phys. Rev. D 107, 083032 (2023).
  33. Y. Lu, Z. S. C. Picker, and A. Kusenko, Direct collapse supermassive black holes from relic particle decay, Phys. Rev. Lett. 133, 091001 (2024).
  34. Y. Lu, Z. S. C. Picker, and A. Kusenko, High-redshift supermassive black holes from tiny black hole explosions, Phys. Rev. D 109, 123016 (2024).
  35. K. Omukai, Primordial star formation under far-ultraviolet radiation, Astrophys. J. 546, 635 (2001).
  36. S. P. Oh and Z. Haiman, Second-generation objects in the universe: Radiative cooling and collapse of halos with virial temperatures above 104 kelvin, Astrophys. J. 569, 558 (2002).
  37. M. C. Begelman, M. Volonteri, and M. J. Rees, Formation of supermassive black holes by direct collapse in pregalactic halos, Mon. Not. R. Astron. Soc. 370, 289 (2006).
  38. K. Inayoshi, E. Visbal, and Z. Haiman, The assembly of the first massive black holes, Annu. Rev. Astron. Astrophys. 58, 27 (2020).
  39. V. Bromm and A. Loeb, Formation of the first supermassive black holes, Astrophys. J. 596, 34 (2003).
  40. J.-H. Choi, I. Shlosman, and M. C. Begelman, Supermassive black hole formation at high redshifts via direct collapse: Physical processes in the early stage, Astrophys. J. 774, 149 (2013).
  41. C. Shang, G. L. Bryan, and Z. Haiman, Supermassive black hole formation by direct collapse: Keeping protogalactic gas h2 free in dark matter haloes with virial temperatures Tvir>rsim104 k, Mon. Not. R. Astron. Soc. 402, 1249 (2010).
  42. M. Dijkstra, Z. Haiman, A. Mesinger, and S. Wyithe, Fluctuations in the high-redshift Lyman-Werner background: Close halo pairs as the origin of supermassive black holes, Mon. Not. R. Astron. Soc. 391, 1961 (2008).
  43. F. Becerra, F. Marinacci, V. Bromm, and L. E. Hernquist, Assembly of supermassive black hole seeds, Mon. Not. R. Astron. Soc. 480, 5029 (2018).
  44. A. Bogdan et al., Evidence for heavy-seed origin of early supermassive black holes from a z≈10 x-ray quasar, Nat. Astron. 8, 126 (2024).
  45. H. Übler, R. Maiolino, E. Curtis-Lake, P. G. Pérez-González, M. Curti, M. Perna et al., GA-NIFS: A massive black hole in a low-metallicity AGN at z 5.55 revealed by JWST/NIRSpec IFS, Astron. Astrophys. 677, A145 (2023).
  46. R. L. Larson, S. L. Finkelstein, D. D. Kocevski, T. A. Hutchison, J. R. Trump, P. A. Haro et al., A ceers discovery of an accreting supermassive black hole 570 myr after the big bang: Identifying a progenitor of massive z>6 quasars, Astrophys. J. Lett. 953, L29 (2023).
  47. Y. Harikane, Y. Zhang, K. Nakajima, M. Ouchi, Y. Isobe, Y. Ono, S. Hatano, Y. Xu, and H. Umeda, A JWST/NIRSpec first census of broad-line AGNs at z = 4–7: Detection of 10 faint AGNs with mBH106−108m⊙ and their host galaxy properties, Astrophys. J. 959, 39 (2023).
  48. A. C. Carnall, R. J. McLure, J. S. Dunlop, D. J. McLeod, V. Wild, F. Cullen et al., A massive quiescent galaxy at redshift 4.658, Nature (London) 619, 716 (2023).
  49. M. Onoue, K. Inayoshi, X. Ding, W. Li, Z. Li, J. Molina, A. K. Inoue, L. Jiang, and L. C. Ho, A candidate for the least-massive black hole in the first 1.1 billion years of the universe, Astrophys. J. Lett. 942, L17 (2023).
  50. D. D. Kocevski, M. Onoue, K. Inayoshi, J. R. Trump, P. A. Haro, A. Grazian et al., Hidden little monsters: Spectroscopic identification of low-mass, broad-line AGNs at z>5 with ceers, Astrophys. J. Lett. 954, L4 (2023).
  51. R. Maiolino et al., A small and vigorous black hole in the early Universe, Nature (London) 627, 59 (2024).
  52. X. Fan, E. Bañados, and R. A. Simcoe, Quasars and the intergalactic medium at cosmic dawn, Annu. Rev. Astron. Astrophys. 61, 373 (2023).
  53. N. Arkani-Hamed, L. Motl, A. Nicolis, and C. Vafa, The string landscape, black holes and gravity as the weakest force, J. High Energy Phys. 06 (2007) 060.
  54. M. Dine, W. Fischler, and M. Srednicki, A simple solution to the strong CP problem with a harmless axion, Phys. Lett. 104B, 199 (1981).
  55. A. R. Zhitnitsky, On possible suppression of the axion hadron interactions. (In Russian), Sov. J. Nucl. Phys. 31, 260 (1980).
  56. S. Bertolini, L. Di Luzio, H. Kolešová, and M. Malinský, Massive neutrinos and invisible axion minimally connected, Phys. Rev. D 91, 055014 (2015).
  57. D. Espriu, F. Mescia, and A. Renau, Axion-Higgs interplay in the two Higgs-doublet model, Phys. Rev. D 92, 095013 (2015).
  58. L. Di Luzio, A. W. M. Guerrera, X. P. Díaz, and S. Rigolin, On the IR/UV flavour connection in non-universal axion models, J. High Energy Phys. 06 (2023) 046.
  59. J. F. Gunion and H. E. Haber, The CP conserving two Higgs doublet model: The approach to the decoupling limit, Phys. Rev. D 67, 075019 (2003).
  60. J. Bernon, J. F. Gunion, H. E. Haber, Y. Jiang, and S. Kraml, Scrutinizing the alignment limit in two-Higgs-doublet models. II. mH=125  GeV, Phys. Rev. D 93, 035027 (2016).
  61. ATLAS Collaboration, Search for heavy neutral Higgs bosons decaying into a top quark pair in 140  fb−1 of proton-proton collision data at s=13  TeV with the ATLAS detector, J. High Energy Phys. 08 (2024) 013.
  62. A. Beniwal, F. Rajec, M. T. Prim, P. Scott, W. Su, M. White et al., Global fit of 2HDM with future collider results, in Snowmass 2021 (2022), arXiv:2203.07883.
  63. G. Arcadi, N. Benincasa, A. Djouadi, and K. Kannike, Two-Higgs-doublet-plus-pseudoscalar model: Collider, dark matter, and gravitational wave signals, Phys. Rev. D 108, 055010 (2023).
  64. J. Dutta, J. Lahiri, C. Li, G. Moortgat-Pick, S. F. Tabira, and J. A. Ziegler, Search for dark matter in 2HDMS at LHC and future lepton colliders, arXiv:2504.14529.
  65. R. R. Volkas, A. J. Davies, and G. C. Joshi, Naturalness of the invisible axion model, Phys. Lett. B 215, 133 (1988).
  66. R. Foot, A. Kobakhidze, K. L. McDonald, and R. R. Volkas, Poincaré protection for a natural electroweak scale, Phys. Rev. D 89, 115018 (2014).
  67. S. B. Giddings and A. Strominger, Axion induced topology change in quantum gravity and string theory, Nucl. Phys. B306, 890 (1988).
  68. R. Alonso and A. Urbano, Wormholes and masses for Goldstone bosons, J. High Energy Phys. 02 (2019) 136.
  69. W. Buchmuller, P. Di Bari, and M. Plumacher, Leptogenesis for pedestrians, Ann. Phys. (Amsterdam) 315, 305 (2005).
  70. G. F. Giudice, A. Notari, M. Raidal, A. Riotto, and A. Strumia, Towards a complete theory of thermal leptogenesis in the SM and MSSM, Nucl. Phys. B685, 89 (2004).
  71. S. Davidson and A. Ibarra, A lower bound on the right-handed neutrino mass from leptogenesis, Phys. Lett. B 535, 25 (2002).
  72. J. Heeck and D. Teresi, Cold keV dark matter from decays and scatterings, Phys. Rev. D 96, 035018 (2017).
  73. I. M. Bloch, A. Caputo, R. Essig, D. Redigolo, M. Sholapurkar, and T. Volansky, Exploring new physics with O(keV) electron recoils in direct detection experiments, J. High Energy Phys. 01 (2021) 178.
  74. A. de Giorgi, L. Merlo, X. Ponce Díaz, and S. Rigolin, The minimal massive Majoron seesaw model, J. High Energy Phys. 03 (2024) 094.
  75. C. A. J. O’Hare, Cosmology of axion dark matter, Proc. Sci. COSMICWISPers (2024) 040 [arXiv:2403.17697].
  76. H. Wang et al., Spectroscopic search for optical emission lines from dark matter decay, Phys. Rev. D 110, 103007 (2024).
  77. J. L. Bernal, A. Caputo, G. Sato-Polito, J. Mirocha, and M. Kamionkowski, Seeking dark matter with γ-ray attenuation, Phys. Rev. D 107, 103046 (2023).
  78. B. Bolliet, J. Chluba, and R. Battye, Spectral distortion constraints on photon injection from low-mass decaying particles, Mon. Not. R. Astron. Soc. 507, 3148 (2021).
  79. D. Wadekar and Z. Wang, Strong constraints on decay and annihilation of dark matter from heating of gas-rich dwarf galaxies, Phys. Rev. D 106, 075007 (2022).
  80. R. Janish and E. Pinetti, Hunting dark matter lines in the infrared background with the James webb space telescope, Phys. Rev. Lett. 134, 071002 (2025).
  81. S. Roy, C. Blanco, C. Dessert, A. Prabhu, and T. Temim, Sensitivity of JWST to eV-scale decaying axion dark matter, Phys. Rev. Lett. 134, 071003 (2025).
  82. A. K. Saha, S. Bouri, A. Das, A. Dubey, and R. Laha, Shedding infrared light on QCD axion and ALP dark matter with JWST, arXiv:2503.14582.
  83. T. Ohkubo, K. Nomoto, H. Umeda, N. Yoshida, and S. Tsuruta, Evolution of very massive Population III stars with mass accretion from pre-main sequence to collapse, Astrophys. J. 706, 1184 (2009).
  84. N. Banik, J. C. Tan, and P. Monaco, The formation of supermassive black holes from Population III.1 seeds. I. Cosmic formation histories and clustering properties, Mon. Not. R. Astron. Soc. 483, 3592 (2019).
  85. P. Kroupa, L. Subr, T. Jerabkova, and L. Wang, Very high redshift quasars and the rapid emergence of supermassive black holes, Mon. Not. R. Astron. Soc. 498, 5652 (2020).
  86. F. Huško, C. G. Lacey, W. J. Roper, J. Schaye, J. M. Briggs, and M. Schaller, The effects of super-eddington accretion and feedback on the growth of early supermassive black holes and galaxies, Mon. Not. R. Astron. Soc. 537, 2559 (2025).
  87. W. Massonneau, M. Volonteri, Y. Dubois, and R. S. Beckmann, How the super-Eddington regime regulates black hole growth in high-redshift galaxies, Astron. Astrophys. 670, A180 (2023).
  88. A. Friedlander, S. Schon, and A. C. Vincent, Supermassive black hole seeds from sub-keV dark matter, J. Cosmol. Astropart. Phys. 06 (2023) 033.
  89. M. Volonteri, M. Habouzit, and M. Colpi, What if young z >9 JWST galaxies hosted massive black holes?, Mon. Not. R. Astron. Soc. 521, 241 (2023).
  90. R. Schneider, R. Valiante, A. Trinca, L. Graziani, M. Volonteri, and R. Maiolino, Are we surprised to find SMBHs with JWST at z ≥9?, Mon. Not. R. Astron. Soc. 526, 3250 (2023).
  91. Y. Ono, Y. Harikane, M. Ouchi, H. Yajima, M. Abe, Y. Isobe et al., Morphologies of galaxies at z≳9 uncovered by JWST/NIRCAM imaging: Cosmic size evolution and an identification of an extremely compact bright galaxy at z∼12, arXiv:2208.13582.
  92. P. Natarajan, F. Pacucci, A. Ricarte, A. Bogdan, A. D. Goulding, and N. Cappelluti, First detection of an overmassive black hole galaxy UHZ1: Evidence for heavy black hole seed formation from direct collapse, Astrophys. J. Lett. 960, L1 (2024).
  93. O. E. Kovacs et al., A candidate supermassive black hole in a gravitationally lensed galaxy at z≈10, Astrophys. J. Lett. 965, L21 (2024).
  94. B. Cyr, H. Jiao, and R. Brandenberger, Massive black holes at high redshifts from superconducting cosmic strings, Mon. Not. R. Astron. Soc. 517, 2221 (2022).
  95. S. Sethi, Z. Haiman, and K. Pandey, Supermassive black hole formation at high redshifts through a primordial magnetic field, Astrophys. J. 721, 615 (2010).
  96. B. Agarwal, B. Smith, S. Glover, P. Natarajan, and S. Khochfar, New constraints on direct collapse black hole formation in the early universe, Mon. Not. R. Astron. Soc. 459, 4209 (2016).
  97. J. Wolcott-Green, Z. Haiman, and G. L. Bryan, Beyond Jcrit: A critical curve for suppression of H2-cooling in protogalaxies, Mon. Not. R. Astron. Soc. 469, 3329 (2017).
  98. Y. Luo, I. Shlosman, K. Nagamine, and T. Fang, Direct collapse to supermassive black hole seeds: The critical conditions for suppression of h2 cooling, Mon. Not. R. Astron. Soc. 492, 4917 (2020).
  99. B. T. Draine and F. Bertoldi, Structure of stationary photodissociation fronts, Astrophys. J. 468, 269 (1996).
  100. P. R. Shapiro and H. Kang, Hydrogen molecules and the radiative cooling of pregalactic shocks, Astrophys. J. 318, 32 (1987).
  101. J. Jeon, V. Bromm, B. Liu, and S. L. Finkelstein, Physical pathways for JWST-observed supermassive black holes in the early universe, Astrophys. J. 979, 127 (2025).
  102. K. Nakajima and R. Maiolino, Diagnostics for popiii galaxies and direct collapse black holes in the early universe, Mon. Not. R. Astron. Soc. 513, 5134 (2022).
  103. R. Maiolino et al., A black hole in a near-pristine galaxy 700 million years after the Big Bang, arXiv:2505.22567.
  104. C. R. Harris, K. J. Millman, S. J. van der Walt, R. Gommers, P. Virtanen, D. Cournapeau et al., Array programming with numpy, Nature (London) 585, 357 (2020).
  105. P. Virtanen, R. Gommers, T. E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau et al., scipy 1.0: Fundamental algorithms for scientific computing in python, Nat. Methods 17, 261 (2020).
  106. J. D. Hunter, matplotlib: A 2d graphics environment, Comput. Sci. Eng. 9, 90 (2007).

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Phys. Rev. D 113, 015037– Published 23 January, 2026
  • Received 14 July 2025
  • Accepted 5 January 2026
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