- Physical Review Journals
All JournalsPhysics Magazine

Physical Review D

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

How to identify a Majoron: Effective field theories of spontaneous lepton number breaking

Carla Biggio1,2,*, Marta Fuentes Zamoro3,†, Xu Li2,‡, Luca Merlo3,§, and Luca Ottonello1,∥

  • *Contact author: carla.biggio@ge.infn.it
  • †Contact author: marta.zamoro@uam.es
  • ‡Contact author: xu.li@ge.infn.it
  • §Contact author: luca.merlo@uam.es
  • ∥Contact author: S4872814@studenti.unige.it
PDF

Phys. Rev. D 114, 075023 – Published 20 October, 2026

DOI: https://doi.org/10.1103/x5gn-jp4v

Abstract

We revisit the traditional type I, II, and III seesaw mechanisms in the presence of a complex scalar field charged under a global U(1) symmetry that can be identified with lepton number and the Peccei-Quinn symmetry. After symmetry breaking, the radial mode becomes heavy while the angular mode appears as an axionlike particle, traditionally dubbed the Majoron. We construct the effective field theory obtained after integrating out the heavy states and analyze two matching orders: first removing the radial mode and then the seesaw fields, and vice versa. Both procedures yield the same low-energy Lagrangian containing only Standard Model fields and the Majoron. Because a single vacuum expectation value fixes the mediator masses, the radial mode, and every Majoron coupling, these models predict relations among observables rather than their individual size, and it is these relations that are testable. Indeed, the invisible Higgs width is locked to the universal suppression of the Higgs couplings, while the Majoron-lepton coupling is fixed by the measured nonunitarity of the leptonic mixing matrix, and the two independently give comparable lower bounds on the same lepton-number-breaking scale, of the order of 1–10 TeV. Neutrinoless double beta decay with Majoron emission, by contrast, has no sensitivity in this class of models. The framework is, thus, falsifiable even when the new states lie far beyond experimental reach.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (192)

  1. P. Minkowski, μ→eγ at a rate of one out of 109 muon decays?, Phys. Lett. 67B, 421 (1977).
  2. M. Gell-Mann, P. Ramond, and R. Slansky, Complex spinors and unified theories, Conf. Proc. C 790927, 315 (1979).
  3. T. Yanagida, Horizontal gauge symmetry and masses of neutrinos, Conf. Proc. C 7902131, 95 (1979).
  4. R. N. Mohapatra and G. Senjanovic, Neutrino mass and spontaneous parity nonconservation, Phys. Rev. Lett. 44, 912 (1980).
  5. M. Magg and C. Wetterich, Neutrino mass problem and gauge hierarchy, Phys. Lett. 94B, 61 (1980).
  6. J. Schechter and J. W. F. Valle, Neutrino masses in SU(2)×U(1) theories, Phys. Rev. D 22, 2227 (1980).
  7. T. P. Cheng and L.-F. Li, Neutrino masses, mixings and oscillations in SU(2)×U(1) models of electroweak interactions, Phys. Rev. D 22, 2860 (1980).
  8. G. Lazarides, Q. Shafi, and C. Wetterich, Proton lifetime and fermion masses in an SO(10) model, Nucl. Phys. B181, 287 (1981).
  9. R. N. Mohapatra and G. Senjanovic, Neutrino masses and mixings in gauge models with spontaneous parity violation, Phys. Rev. D 23, 165 (1981).
  10. C. Wetterich, Neutrino masses and the scale of B-L violation, Nucl. Phys. B187, 343 (1981).
  11. R. Foot, H. Lew, X. G. He, and G. C. Joshi, Seesaw neutrino masses induced by a triplet of leptons, Z. Phys. C 44, 441 (1989).
  12. D. Wyler and L. Wolfenstein, Massless neutrinos in left-right symmetric models, Nucl. Phys. B218, 205 (1983).
  13. R. N. Mohapatra and J. W. F. Valle, Neutrino mass and baryon number nonconservation in superstring models, Phys. Rev. D 34, 1642 (1986).
  14. J. Bernabeu, A. Santamaria, J. Vidal, A. Mendez, and J. W. F. Valle, Lepton flavor nonconservation at high-energies in a superstring inspired standard model, Phys. Lett. B 187, 303 (1987).
  15. M. Malinsky, J. C. Romao, and J. W. F. Valle, Novel supersymmetric SO(10) seesaw mechanism, Phys. Rev. Lett. 95, 161801 (2005).
  16. J. Kersten and A. Y. Smirnov, Right-handed neutrinos at CERN LHC and the mechanism of neutrino mass generation, Phys. Rev. D 76, 073005 (2007).
  17. A. Abada, C. Biggio, F. Bonnet, M. B. Gavela, and T. Hambye, Low energy effects of neutrino masses, J. High Energy Phys. 12 (2007) 061.
  18. R. D. Peccei and H. R. Quinn, CP conservation in the presence of instantons, Phys. Rev. Lett. 38, 1440 (1977).
  19. S. Weinberg, A new light boson?, Phys. Rev. Lett. 40, 223 (1978).
  20. F. Wilczek, Problem of strong P and T invariance in the presence of instantons, Phys. Rev. Lett. 40, 279 (1978).
  21. A. R. Zhitnitsky, On possible suppression of the axion hadron interactions, Yad. Fiz. 31, 497 (1980) [Sov. J. Nucl. Phys. 31, 260 (1980)].
  22. M. Dine, W. Fischler, and M. Srednicki, A simple solution to the strong CP problem with a harmless axion, Phys. Lett. 104B, 199 (1981).
  23. J. E. Kim, Weak interaction singlet and strong CP invariance, Phys. Rev. Lett. 43, 103 (1979).
  24. M. A. Shifman, A. I. Vainshtein, and V. I. Zakharov, Can confinement ensure natural CP invariance of strong interactions?, Nucl. Phys. B166, 493 (1980).
  25. L. Di Luzio, F. Mescia, and E. Nardi, Redefining the axion window, Phys. Rev. Lett. 118, 031801 (2017).
  26. L. Di Luzio, F. Mescia, and E. Nardi, Window for preferred axion models, Phys. Rev. D 96, 075003 (2017).
  27. M. K. Gaillard, M. B. Gavela, R. Houtz, P. Quilez, and R. Del Rey, Color unified dynamical axion, Eur. Phys. J. C 78, 972 (2018).
  28. A. Hook, S. Kumar, Z. Liu, and R. Sundrum, High quality QCD axion and the LHC, Phys. Rev. Lett. 124, 221801 (2020).
  29. L. Di Luzio, M. Giannotti, E. Nardi, and L. Visinelli, The landscape of QCD axion models, Phys. Rep. 870, 1 (2020).
  30. L. Di Luzio, R. Gröber, and P. Paradisi, Hunting for CP-violating axionlike particle interactions, Phys. Rev. D 104, 095027 (2021).
  31. L. Di Luzio, B. Gavela, P. Quilez, and A. Ringwald, An even lighter QCD axion, J. High Energy Phys. 05 (2021) 184.
  32. L. Di Luzio, B. Gavela, P. Quilez, and A. Ringwald, Dark matter from an even lighter QCD axion: Trapped misalignment, J. Cosmol. Astropart. Phys. 10 (2021) 001.
  33. B. Gavela, P. Quílez, and M. Ramos, The QCD axion sum rule, J. High Energy Phys. 04 (2024) 056.
  34. P. Cox, T. Gherghetta, and A. Paul, A common origin for the QCD axion and sterile neutrinos from SU(5) strong dynamics, J. High Energy Phys. 12 (2023) 180.
  35. A. de Giorgi and M. Ramos, Extra-dimensional axion patterns, Phys. Rev. D 111, 075006 (2025).
  36. M. Fernández Navarro, M. F. Zamoro, M. Pesut, and X. Ponce Díaz, Structure of multiaxion solutions to the strong CP problem, Phys. Rev. D 114, 035019 (2026).
  37. M. F. Zamoro, Á. Lozano-Onrubia, L. Merlo, and S. Rosende Herrero, Crossing into the ma>fa region for leptophilic ALPs, arXiv:2605.00115.
  38. E. Witten, Some properties of O(32) superstrings, Phys. Lett. 149B, 351 (1984).
  39. K.-S. Choi, I.-W. Kim, and J. E. Kim, String compactification, QCD axion and axion-photon-photon coupling, J. High Energy Phys. 03 (2007) 116.
  40. P. Svrcek and E. Witten, Axions in string theory, J. High Energy Phys. 06 (2006) 051.
  41. A. Arvanitaki, S. Dimopoulos, S. Dubovsky, N. Kaloper, and J. March-Russell, String axiverse, Phys. Rev. D 81, 123530 (2010).
  42. M. Cicoli, M. Goodsell, and A. Ringwald, The type IIB string axiverse and its low-energy phenomenology, J. High Energy Phys. 10 (2012) 146.
  43. B. Bellazzini, A. Mariotti, D. Redigolo, F. Sala, and J. Serra, R-axion at colliders, Phys. Rev. Lett. 119, 141804 (2017).
  44. L. Merlo, F. Pobbe, and S. Rigolin, The minimal axion minimal linear σ model, Eur. Phys. J. C 78, 415 (2018); 79, 963(E) (2019).
  45. I. Brivio, M. B. Gavela, S. Pascoli, R. del Rey, and S. Saa, The axion and the Goldstone Higgs, Chin. J. Phys. 61, 55 (2019).
  46. J. Alonso-González, L. Merlo, F. Pobbe, S. Rigolin, and O. Sumensari, Testable axion-like particles in the minimal linear σ model, Nucl. Phys. B950, 114839 (2020).
  47. J. Alonso-Gonzalez, J. M. Lizana, V. Martinez-Fernandez, L. Merlo, and S. Pokorski, Probing effective field theory approach in the CP violating minimal linear σ model, Eur. Phys. J. C 81, 538 (2021).
  48. G. Gelmini, D. N. Schramm, and J. W. F. Valle, Majorons: A simultaneous solution to the large and small scale dark matter problems, Phys. Lett. 146B, 311 (1984).
  49. V. Berezinsky and J. W. F. Valle, The KeV Majoron as a dark matter particle, Phys. Lett. B 318, 360 (1993).
  50. M. Lattanzi and J. W. F. Valle, Decaying warm dark matter and neutrino masses, Phys. Rev. Lett. 99, 121301 (2007).
  51. 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.
  52. 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).
  53. 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).
  54. K. Akita, K. Hamaguchi, H. Kitagawa, and T. Yokoyama, Minimal Majoron dark matter, arXiv:2605.12946.
  55. A. de Giorgi, D. Naredo-Tuero, and X. Ponce Díaz, The Majoron cosmological window: Dark matter and thermal leptogenesis, arXiv:2605.18944.
  56. B. Batell, A. Dasgupta, S. Dutta, and A. Ghalsasi, Majoron dark matter, high-scale seesaw framework, and leptogenesis, Phys. Rev. D 114, 055018 (2026).
  57. R. Z. Ferreira and A. Notari, Observable windows for the QCD axion through the number of relativistic species, Phys. Rev. Lett. 120, 191301 (2018).
  58. F. D’Eramo, R. Z. Ferreira, A. Notari, and J. L. Bernal, Hot axions and the H0 tension, J. Cosmol. Astropart. Phys. 11 (2018) 014.
  59. M. Escudero and S. J. Witte, A CMB search for the neutrino mass mechanism and its relation to the Hubble tension, Eur. Phys. J. C 80, 294 (2020).
  60. F. Arias-Aragón, F. D’eramo, R. Z. Ferreira, L. Merlo, and A. Notari, Cosmic imprints of XENON1T axions, J. Cosmol. Astropart. Phys. 11 (2020) 025.
  61. F. Arias-Aragon, E. Fernandez-Martinez, M. Gonzalez-Lopez, and L. Merlo, Neutrino masses and Hubble tension via a majoron in MFV, Eur. Phys. J. C 81, 28 (2021).
  62. F. Arias-Aragón, F. D’Eramo, R. Z. Ferreira, L. Merlo, and A. Notari, Production of thermal axions across the ElectroWeak phase transition, J. Cosmol. Astropart. Phys. 03 (2021) 090.
  63. R. Z. Ferreira, A. Notari, and F. Rompineve, Dine-Fischler-Srednicki-Zhitnitsky axion in the CMB, Phys. Rev. D 103, 063524 (2021).
  64. M. Escudero and S. J. Witte, The Hubble tension as a hint of leptogenesis and neutrino mass generation, Eur. Phys. J. C 81, 515 (2021).
  65. T. Araki, K. Asai, K. Honda, R. Kasuya, J. Sato, T. Shimomura, and M. J. S. Yang, Resolving the Hubble tension in a U(1)Lμ−Lτ model with the Majoron, Prog. Theor. Exp. Phys. 2021, 103B05 (2021).
  66. F. D’Eramo, F. Hajkarim, and S. Yun, Thermal axion production at low temperatures: A smooth treatment of the QCD phase transition, Phys. Rev. Lett. 128, 152001 (2022).
  67. F. D’Eramo, F. Hajkarim, and S. Yun, Thermal QCD axions across thresholds, J. High Energy Phys. 10 (2021) 224.
  68. F. D’Eramo, E. Di Valentino, W. Giarè, F. Hajkarim, A. Melchiorri, O. Mena, F. Renzi, and S. Yun, Cosmological bound on the QCD axion mass, redux, J. Cosmol. Astropart. Phys. 09 (2022) 022.
  69. A. Davidson and K. C. Wali, Minimal flavor unification via multigenerational Peccei-Quinn symmetry, Phys. Rev. Lett. 48, 11 (1982).
  70. F. Wilczek, Axions and family symmetry breaking, Phys. Rev. Lett. 49, 1549 (1982).
  71. Y. Ema, K. Hamaguchi, T. Moroi, and K. Nakayama, Flaxion: A minimal extension to solve puzzles in the standard model, J. High Energy Phys. 01 (2017) 096.
  72. L. Calibbi, F. Goertz, D. Redigolo, R. Ziegler, and J. Zupan, Minimal axion model from flavor, Phys. Rev. D 95, 095009 (2017).
  73. F. Arias-Aragon and L. Merlo, The minimal flavour violating axion, J. High Energy Phys. 10 (2017) 168; 11 (2019) 152(E).
  74. F. Arias-Aragón, E. Fernández-Martínez, M. González-López, and L. Merlo, Dynamical minimal flavour violating inverse Seesaw, J. High Energy Phys. 09 (2022) 210.
  75. 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.
  76. A. Greljo, A. Smolkovič, and A. Valenti, Froggatt-Nielsen ALP, J. High Energy Phys. 09 (2024) 174.
  77. C. Albertus et al., WISPedia—the WISPs Encyclopedia: Cosmic WISPers 2026—V1.0, arXiv:2602.09089.
  78. K. Choi, K. Kang, and J. E. Kim, Effects of η′ in low-energy axion physics, Phys. Lett. B 181, 145 (1986).
  79. A. Salvio, A. Strumia, and W. Xue, Thermal axion production, J. Cosmol. Astropart. Phys. 01 (2014) 011.
  80. I. Brivio, M. B. Gavela, L. Merlo, K. Mimasu, J. M. No, R. del Rey, and V. Sanz, ALPs effective field theory and collider signatures, Eur. Phys. J. C 77, 572 (2017).
  81. G. Alonso-Álvarez, M. B. Gavela, and P. Quilez, Axion couplings to electroweak gauge bosons, Eur. Phys. J. C 79, 223 (2019).
  82. M. B. Gavela, R. Houtz, P. Quilez, R. Del Rey, and O. Sumensari, Flavor constraints on electroweak ALP couplings, Eur. Phys. J. C 79, 369 (2019).
  83. M. Chala, G. Guedes, M. Ramos, and J. Santiago, Running in the ALPs, Eur. Phys. J. C 81, 181 (2021).
  84. J. Bonilla, I. Brivio, M. B. Gavela, and V. Sanz, One-loop corrections to ALP couplings, J. High Energy Phys. 11 (2021) 168.
  85. F. Arias-Aragón and C. Smith, Leptoquarks, axions and the unification of B, L, and Peccei-Quinn symmetries, Phys. Rev. D 106, 055034 (2022).
  86. F. Arias-Aragón, J. Quevillon, and C. Smith, Axion-like ALPs, J. High Energy Phys. 03 (2023) 134.
  87. L. Di Luzio, G. Levati, and P. Paradisi, The chiral Lagrangian of CP-violating axion-like particles, J. High Energy Phys. 02 (2024) 020.
  88. L. Di Luzio, H. Gisbert, G. Levati, P. Paradisi, and P. Sørensen, CP-violating axions: A theory review, arXiv:2312.17310.
  89. J. Jaeckel, M. Jankowiak, and M. Spannowsky, LHC probes the hidden sector, Phys. Dark Universe 2, 111 (2013).
  90. K. Mimasu and V. Sanz, ALPs at colliders, J. High Energy Phys. 06 (2015) 173.
  91. J. Jaeckel and M. Spannowsky, Probing MeV to 90 GeV axion-like particles with LEP and LHC, Phys. Lett. B 753, 482 (2016).
  92. A. Alves, A. G. Dias, and K. Sinha, Diphotons at the Z-pole in models of the 750 GeV resonance decaying to axion-like particles, J. High Energy Phys. 08 (2016) 060.
  93. S. Knapen, T. Lin, H. K. Lou, and T. Melia, Searching for axionlike particles with ultraperipheral Heavy-Ion collisions, Phys. Rev. Lett. 118, 171801 (2017).
  94. M. Bauer, M. Neubert, and A. Thamm, LHC as an axion factory: Probing an axion explanation for (g−2)μ with exotic Higgs decays, Phys. Rev. Lett. 119, 031802 (2017).
  95. A. Mariotti, D. Redigolo, F. Sala, and K. Tobioka, New LHC bound on low-mass diphoton resonances, Phys. Lett. B 783, 13 (2018).
  96. M. Bauer, M. Neubert, and A. Thamm, Collider probes of axion-like particles, J. High Energy Phys. 12 (2017) 044.
  97. C. Baldenegro, S. Fichet, G. von Gersdorff, and C. Royon, Searching for axion-like particles with proton tagging at the LHC, J. High Energy Phys. 06 (2018) 131.
  98. N. Craig, A. Hook, and S. Kasko, The photophobic ALP, J. High Energy Phys. 09 (2018) 028.
  99. M. Bauer, M. Heiles, M. Neubert, and A. Thamm, Axion-like particles at future colliders, Eur. Phys. J. C 79, 74 (2019).
  100. M. B. Gavela, J. M. No, V. Sanz, and J. F. de Trocóniz, Nonresonant searches for axionlike particles at the LHC, Phys. Rev. Lett. 124, 051802 (2020).
  101. G. Haghighat, D. Haji Raissi, and M. Mohammadi Najafabadi, New collider searches for axionlike particles coupling to gluons, Phys. Rev. D 102, 115010 (2020).
  102. D. Wang, L. Wu, J. M. Yang, and M. Zhang, Photon-jet events as a probe of axionlike particles at the LHC, Phys. Rev. D 104, 095016 (2021).
  103. A. de Giorgi, L. Merlo, and J.-L. Tastet, Probing HNL-ALP couplings at colliders, Fortschr. Phys. 71, 2300027 (2023).
  104. J. Bonilla, I. Brivio, J. Machado-Rodríguez, and J. F. de Trocóniz, Nonresonant searches for axion-like particles in vector boson scattering processes at the LHC, J. High Energy Phys. 06 (2022) 113.
  105. F. A. Ghebretinsaea, Z. S. Wang, and K. Wang, Probing axion-like particles coupling to gluons at the LHC, J. High Energy Phys. 07 (2022) 070.
  106. V. E. Vileta, B. Gavela, R. Houtz, and P. Quilez, Discrete Goldstone bosons, Phys. Rev. D 107, 035009 (2023).
  107. L. Calibbi, Z. Huang, S. Qin, Y. Yang, and X. Yin, Testing axion couplings to leptons in Z decays at future e+e- colliders, Phys. Rev. D 108, 015002 (2023).
  108. M. B. Marcos, A. de Giorgi, L. Merlo, and J.-L. Tastet, ALPs and HNLs at LHC and muon colliders: Uncovering new couplings and signals, SciPost Phys. 18, 084 (2025).
  109. F. Arias-Aragón, L. Darmé, G. G. di Cortona, and E. Nardi, Atoms as electron accelerators for measuring the cross section of e+e−→hadrons, Phys. Rev. Lett. 134, 061802 (2025).
  110. A. Biekötter and K. Mimasu, Axions and axion-like particles: Collider searches, Encycl. Part. Phys. 3, 673 (2026).
  111. Y. Ema, P. J. Fox, M. Hostert, T. Menzo, M. Pospelov, A. Ray, and J. Zupan, Long-lived axionlike particles from tau decays, Phys. Rev. D 112, 115028 (2025).
  112. S. Bhattacharya, S. Jahedi, S. K. Manna, and A. Sil, Probing ALP-portal fermionic dark matter at the e+e− colliders, Phys. Rev. D 113, 115015 (2026).
  113. E. Izaguirre, T. Lin, and B. Shuve, Searching for axionlike particles in flavor-changing neutral current processes, Phys. Rev. Lett. 118, 111802 (2017).
  114. W. J. Marciano, A. Masiero, P. Paradisi, and M. Passera, Contributions of axionlike particles to lepton dipole moments, Phys. Rev. D 94, 115033 (2016).
  115. L. Merlo, F. Pobbe, S. Rigolin, and O. Sumensari, Revisiting the production of ALPs at B-factories, J. High Energy Phys. 06 (2019) 091.
  116. D. Aloni, C. Fanelli, Y. Soreq, and M. Williams, Photoproduction of axionlike particles, Phys. Rev. Lett. 123, 071801 (2019).
  117. M. Bauer, M. Neubert, S. Renner, M. Schnubel, and A. Thamm, Axionlike particles, lepton-flavor violation, and a new explanation of aμ and ae, Phys. Rev. Lett. 124, 211803 (2020).
  118. C. Cornella, P. Paradisi, and O. Sumensari, Hunting for ALPs with lepton flavor violation, J. High Energy Phys. 01 (2020) 158.
  119. M. Bauer, M. Neubert, S. Renner, M. Schnubel, and A. Thamm, The low-energy effective theory of axions and ALPs, J. High Energy Phys. 04 (2021) 063.
  120. L. Calibbi, D. Redigolo, R. Ziegler, and J. Zupan, Looking forward to lepton-flavor-violating ALPs, J. High Energy Phys. 09 (2021) 173.
  121. M. Bauer, M. Neubert, S. Renner, M. Schnubel, and A. Thamm, Flavor probes of axion-like particles, J. High Energy Phys. 09 (2022) 056.
  122. A. Carmona, C. Scherb, and P. Schwaller, Charming ALPs, J. High Energy Phys. 08 (2021) 121.
  123. A. W. M. Guerrera and S. Rigolin, Revisiting K→πa decays, Eur. Phys. J. C 82, 192 (2022).
  124. J. Alda, A. W. M. Guerrera, S. Peñaranda, and S. Rigolin, Leptonic meson decays into invisible ALP, Nucl. Phys. B979, 115791 (2022).
  125. E. Bertholet, S. Chakraborty, V. Loladze, T. Okui, A. Soffer, and K. Tobioka, Heavy QCD axion at Belle II: Displaced and prompt signals, Phys. Rev. D 105, L071701 (2022).
  126. H.-C. Cheng, L. Li, and E. Salvioni, A theory of dark pions, J. High Energy Phys. 01 (2022) 122.
  127. J. Bonilla, A. de Giorgi, B. Gavela, L. Merlo, and M. Ramos, The cost of an ALP solution to the neutral B-anomalies, J. High Energy Phys. 02 (2023) 138.
  128. J. Bonilla, A. de Giorgi, and M. Ramos, Neutral B-anomalies from an on-shell scalar exchange, arXiv:2211.05135.
  129. A. de Giorgi and G. Piazza, A Lesson from RττK(*) and RννK(*) at Belle II, Fortschr. Phys. 72, 2300200 (2024).
  130. A. W. M. Guerrera and S. Rigolin, ALP production in weak mesonic decays, Fortschr. Phys. 71, 2200192 (2023).
  131. J. Bonilla, B. Gavela, and J. Machado-Rodríguez, Limits on ALP-neutrino couplings from loop-level processes, Phys. Rev. D 109, 055023 (2024).
  132. F. Arias-Aragón, V. Brdar, and J. Quevillon, New directions for axionlike particle searches combining nuclear reactors and haloscopes, Phys. Rev. Lett. 132, 211802 (2024).
  133. L. Di Luzio, A. W. M. Guerrera, X. Ponce Díaz, and S. Rigolin, Axion-like particles in radiative quarkonia decays, J. High Energy Phys. 06 (2024) 217.
  134. A. de Giorgi, M. Fuentes Zamoro, and L. Merlo, Visible GeV ALP from TeV vector-like leptons, Fortschr. Phys. 73, 2400165 (2025).
  135. J. Alda, G. Levati, P. Paradisi, S. Rigolin, and N. Selimovic, Collider and astrophysical signatures of light scalars with enhanced τ couplings, J. High Energy Phys. 06 (2025) 008.
  136. J. Alda, C. Broggini, G. Di Carlo, L. Di Luzio, D. Piatti, S. Rigolin, and C. Toni, Weak nuclear decays deep-underground as a probe of axion dark matter, Phys. Rev. D 111, 035022 (2025).
  137. F. Arias-Aragón, L. Darmé, G. G. di Cortona, and E. Nardi, Production of dark sector particles via resonant positron annihilation on atomic electrons, Phys. Rev. Lett. 132, 261801 (2024); 133, 219901(E) (2024).
  138. F. Arias-Aragón, M. Giannotti, G. G. di Cortona, and F. Mescia, Axion-induced pair production: A new strategy for axion detection, Phys. Rev. D 111, 043021 (2025).
  139. D. Bisht, S. Chakraborty, and A. Samanta, A comprehensive study of ALPs from B-decays, J. High Energy Phys. 07 (2025) 092.
  140. L. Calibbi, T. Li, L. Mukherjee, and Y. Yang, Probing ALP lepton flavor violation at μTRISTAN, Phys. Rev. D 110, 115009 (2024).
  141. J. Martin Camalich and R. Ziegler, Flavor phenomenology of light dark sectors, Annu. Rev. Nucl. Part. Sci. 75, 223 (2025).
  142. J. Alda, M. Fuentes Zamoro, L. Merlo, X. Ponce Díaz, and S. Rigolin, Comprehensive ALP searches in meson decays, arXiv:2507.19578.
  143. J. Alda, M. Fuentes Zamoro, L. Merlo, X. Ponce Díaz, and S. Rigolin, ALPaca: The ALP automatic computing algorithm, arXiv:2508.08354.
  144. M. Ardu, L. Calibbi, M. Fedele, and F. Mescia, ALP production in lepton flavour violating meson, tau and gauge boson decays, J. High Energy Phys. 08 (2026) 217.
  145. A. Arza et al., The COSMIC WISPers white paper: The physics case for weakly interacting slim particles, arXiv:2603.03433.
  146. 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).
  147. Y. Chikashige, R. N. Mohapatra, and R. D. Peccei, Are there real Goldstone bosons associated with broken lepton number?, Phys. Lett. 98B, 265 (1981).
  148. G. B. Gelmini and M. Roncadelli, Left-Handed neutrino mass scale and spontaneously broken lepton number, Phys. Lett. 99B, 411 (1981).
  149. C. Biggio, L. Calibbi, T. Ota, and S. Zanchini, Majoron dark matter from a type II seesaw model, Phys. Rev. D 108, 115003 (2023).
  150. H. Debnath, P. Fileviez Perez, and K. Gonzalez-Quesada, Majorana neutrinos and dark matter from anomaly cancellation, Phys. Rev. D 109, 115030 (2024).
  151. A. de Giorgi, L. Merlo, X. Ponce Díaz, and S. Rigolin, The minimal massive majoron seesaw model, J. High Energy Phys. 03 (2024) 094.
  152. Q. Liang, X. Ponce Díaz, and T. T. Yanagida, Axion detection experiments can probe majoron models, Phys. Rev. Lett. 134, 151803 (2025).
  153. 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.
  154. H. Debnath, P. Fileviez Perez, and G. Miller, The QCD axion and neutrino masses, arXiv:2608.05150.
  155. A. Palavrić, X. Ponce Díaz, and H. Tiblom, The KSVZ Atlas: A unified SMEFT-ALP framework. arXiv:2606.12298.
  156. A. Anisimov, Majorana dark matter, in The Identification of Dark Matter (World Scientific, Singapore, 2006), 12, pp. 439–449.
  157. M. L. Graesser, Broadening the Higgs boson with right-handed neutrinos and a higher dimension operator at the electroweak scale, Phys. Rev. D 76, 075006 (2007).
  158. M. L. Graesser, Experimental constraints on Higgs boson decays to TeV-scale right-handed neutrinos, arXiv:0705.2190.
  159. F. del Aguila, S. Bar-Shalom, A. Soni, and J. Wudka, Heavy Majorana neutrinos in the effective Lagrangian description: Application to hadron colliders, Phys. Lett. B 670, 399 (2009).
  160. A. Aparici, K. Kim, A. Santamaria, and J. Wudka, Right-handed neutrino magnetic moments, Phys. Rev. D 80, 013010 (2009).
  161. Y. Liao and X.-D. Ma, Operators up to dimension seven in standard model effective field theory extended with sterile neutrinos, Phys. Rev. D 96, 015012 (2017).
  162. S. Bhattacharya and J. Wudka, Dimension-seven operators in the standard model with right handed neutrinos, Phys. Rev. D 94, 055022 (2016); 95, 039904(E) (2017).
  163. H.-L. Li, Z. Ren, M.-L. Xiao, J.-H. Yu, and Y.-H. Zheng, Operator bases in effective field theories with sterile neutrinos: d≤9, J. High Energy Phys. 11 (2021) 003.
  164. B. Grzadkowski, M. Iskrzynski, M. Misiak, and J. Rosiek, Dimension-six terms in the standard model Lagrangian, J. High Energy Phys. 10 (2010) 085.
  165. R. Balkin, M. Ruhdorfer, E. Salvioni, and A. Weiler, Dark matter shifts away from direct detection, J. Cosmol. Astropart. Phys. 11 (2018) 050.
  166. S. Weinberg, Baryon and lepton nonconserving processes, Phys. Rev. Lett. 43, 1566 (1979).
  167. A. Broncano, M. B. Gavela, and E. E. Jenkins, The effective Lagrangian for the seesaw model of neutrino mass and leptogenesis, Phys. Lett. B 552, 177 (2003); 636, 332(E) (2006).
  168. M. Blennow, E. Fernández-Martínez, J. Hernández-García, J. López-Pavón, X. Marcano, and D. Naredo-Tuero, Bounds on lepton non-unitarity and heavy neutrino mixing, J. High Energy Phys. 08 (2023) 030.
  169. Y. Cheng, C.-W. Chiang, X.-G. He, and J. Sun, Flavor-changing Majoron interactions with leptons, Phys. Rev. D 104, 013001 (2021).
  170. J. Sun, Y. Cheng, and X.-G. He, Structure of flavor changing Goldstone boson interactions, J. High Energy Phys. 04 (2021) 141.
  171. A. Arhrib, R. Benbrik, M. Chabab, G. Moultaka, M. C. Peyranere, L. Rahili, and J. Ramadan, The Higgs potential in the type II seesaw model, Phys. Rev. D 84, 095005 (2011).
  172. G. Moultaka and M. C. Peyranère, Vacuum stability conditions for Higgs potentials with SU(2)L triplets, Phys. Rev. D 103, 115006 (2021).
  173. X. Li, D. Zhang, and S. Zhou, One-loop matching of the type-II seesaw model onto the standard model effective field theory, J. High Energy Phys. 04 (2022) 038.
  174. X. Ponce Díaz, ΔEFT: An effective field theory of the type-2 Seesaw mechanism, Talk given at the internal HIDDeN webinar (Universität Heidelberg and Max-Planck-Institut für Kernphysik, 2021), based on the author’s MSc thesis (supervisors: T. Plehn and W. Rodejohann), https://projects.ift.uam-csic.es/hidden-virtual-institute/files/PresentacionHiddenESR_PonceDiaz_Xavier.pdf.
  175. C. Garcia-Cely and J. Heeck, Neutrino lines from Majoron dark matter, J. High Energy Phys. 05 (2017) 102.
  176. J. Heeck and H. H. Patel, Majoron at two loops, Phys. Rev. D 100, 095015 (2019).
  177. E. K. Akhmedov, Z. G. Berezhiani, R. N. Mohapatra, and G. Senjanovic, Planck scale effects on the majoron, Phys. Lett. B 299, 90 (1993).
  178. I. Z. Rothstein, K. S. Babu, and D. Seckel, Planck scale symmetry breaking and majoron physics, Nucl. Phys. B403, 725 (1993).
  179. A. David, A. Denner, M. Duehrssen, M. Grazzini, C. Grojean, G. Passarino, M. Schumacher, M. Spira, G. Weiglein, and M. Zanetti (LHC Higgs Cross Section Working Group Collaboration), LHC HXSWG interim recommendations to explore the coupling structure of a Higgs-like particle, arXiv:1209.0040.
  180. D. de Florian et al. (LHC Higgs Cross Section Working Group Collaboration), Handbook of LHC Higgs cross sections: 4. Deciphering the nature of the Higgs sector, CERN Yellow Rep. Monogr. 2, 1 (2017).
  181. G. Aad et al. (ATLAS Collaboration), Combination of searches for invisible decays of the Higgs boson using 139  fb−1 of proton-proton collision data at s=13  TeV collected with the ATLAS experiment, Phys. Lett. B 842, 137963 (2023).
  182. ATLAS Collaboration, HL-LHC prospects for the measurement of triple-Higgs production in the 6b final state at the ATLAS experiment, ATLAS PUB note, CERN Report No. ATL-PHYS-PUB-2025-003, 2025, https://cds.cern.ch/record/2924772.
  183. CMS Collaboration, Search for nonresonant triple Higgs boson production in the six b-quark final state in proton-proton collisions at s = 13 TeV, CMS physics analysis summary, CERN Report No. CMS-PAS-HIG-24-012, 2025, https://cds.cern.ch/record/2945361.
  184. G. Aad et al. (ATLAS, CMS Collaboration), Highlights of the HL-LHC physics projections by ATLAS and CMS, arXiv:2504.00672.
  185. P. Stylianou and G. Weiglein, Constraints on the trilinear and quartic Higgs couplings from triple Higgs production at the LHC and beyond, Eur. Phys. J. C 84, 366 (2024).
  186. G. Aad et al. (ATLAS Collaboration), A detailed map of Higgs boson interactions by the ATLAS experiment ten years after the discovery, Nature (London) 607, 52 (2022); 612, E24 (2022).
  187. S. Navas et al. (Particle Data Group Collaboration), Review of particle physics, Phys. Rev. D 110, 030001 (2024).
  188. A. Gando et al. (KamLAND-Zen Collaboration), Limits on Majoron-emitting double-beta decays of Xe-136 in the KamLAND-Zen experiment, Phys. Rev. C 86, 021601 (2012).
  189. A. P. Lessa and O. L. G. Peres, Revising limits on neutrino-Majoron couplings, Phys. Rev. D 75, 094001 (2007).
  190. S. Sandner, M. Escudero, and S. J. Witte, Precision CMB constraints on eV-scale bosons coupled to neutrinos, Eur. Phys. J. C 83, 709 (2023).
  191. R. Bayes et al. (TWIST Collaboration), Search for two body muon decay signals, Phys. Rev. D 91, 052020 (2015).
  192. A. Jodidio et al., Search for right-handed currents in muon decay, Phys. Rev. D 34, 1967 (1986); 37, 237(E) (1988).

Outline

Information

Phys. Rev. D 114, 075023– Published 20 October, 2026
  • Received 24 August 2026
  • Accepted 28 September 2026
Crossmark - Check for updates button
Creative Commons Logo

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.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation