- Open Access
Probing scalar-mediated sterile neutrinos with gravitational wave and colliders signals
Phys. Rev. D 113, 095006 – Published 4 May, 2026
DOI: https://doi.org/10.1103/29kg-f6jb
Abstract
We propose a UV-complete extension of the Standard Model in which a gauge-singlet scalar acquires a vacuum expectation value, generates a Majorana mass for a sterile neutrino , and mixes with the Higgs field. This framework addresses neutrino masses via a seesaw mechanism and, for sufficiently large scalar mixing, can also drive a strong first-order electroweak phase transition, producing gravitational-wave (GW) signals potentially detectable by GW observatories. The Higgs– mixing also enhances sterile-neutrino pair production at colliders through -channel exchange of the Higgs and . Owing to the small active–sterile mixing angle, is generically long-lived, yielding characteristic displaced-vertex signatures. The combination of GW observations and displaced-vertex searches at colliders provides complementary cross-checks of the model parameter space.
Physics Subject Headings (PhySH)
Article Text
References (125)
- J. Schechter and J. W. F. Valle, Neutrino masses in theories, Phys. Rev. D 22, 2227 (1980).
- E. Ma, Verifiable radiative seesaw mechanism of neutrino mass and dark matter, Phys. Rev. D 73, 077301 (2006).
- 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).
- S. F. King and C. Luhn, Neutrino mass and mixing with discrete symmetry, Rep. Prog. Phys. 76, 056201 (2013).
- R. N. Mohapatra and G. Senjanovic, Neutrino mass and spontaneous parity nonconservation, Phys. Rev. Lett. 44, 912 (1980).
- M. Gell-Mann, P. Ramond, and R. Slansky, Complex spinors and unified theories, Conf. Proc. C 790927, 315 (1979).
- J. Schechter and J. W. F. Valle, Neutrino decay and spontaneous violation of lepton number, Phys. Rev. D 25, 774 (1982).
- E. K. Akhmedov, M. Lindner, E. Schnapka, and J. W. F. Valle, Left-right symmetry breaking in NJL approach, Phys. Lett. B 368, 270 (1996).
- E. K. Akhmedov, M. Lindner, E. Schnapka, and J. W. F. Valle, Dynamical left-right symmetry breaking, Phys. Rev. D 53, 2752 (1996).
- S. M. Barr, A different seesaw formula for neutrino masses, Phys. Rev. Lett. 92, 101601 (2004).
- N. Aghanim et al. (Planck Collaboration), Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys. 641, A6 (2020); 652, C4(E) (2021).
- E. Di Valentino, S. Gariazzo, and O. Mena, Most constraining cosmological neutrino mass bounds, Phys. Rev. D 104, 083504 (2021).
- J. Kopp, P. A. N. Machado, M. Maltoni, and T. Schwetz, Sterile neutrino oscillations: The global picture, J. High Energy Phys. 05 (2013) 050.
- R. Acciarri et al. (MicroBooNE, LAr1-ND, and ICARUS-WA104 Collaborations), A proposal for a three detector short-baseline neutrino oscillation program in the Fermilab booster neutrino beam, arXiv:1503.01520.
- M. Dentler, A. Hernández-Cabezudo, J. Kopp, P. A. N. Machado, M. Maltoni, I. Martinez-Soler, and T. Schwetz, Updated global analysis of neutrino oscillations in the presence of ev-scale sterile neutrinos, J. High Energy Phys. 08 (2018) 010.
- Y. J. Ko et al. (NEOS Collaboration), Sterile neutrino search at the NEOS experiment, Phys. Rev. Lett. 118, 121802 (2017).
- M. G. Aartsen et al. (IceCube Collaboration), Searches for sterile neutrinos with the IceCube detector, Phys. Rev. Lett. 117, 071801 (2016).
- B. Dasgupta and J. Kopp, Cosmologically safe eV-scale sterile neutrinos and improved dark matter structure, Phys. Rev. Lett. 112, 031803 (2014).
- K. N. Abazajian, Sterile neutrinos in cosmology, Phys. Rep. 711–712, 1 (2017).
- K. Abe et al. (Super-Kamiokande Collaboration), Limits on sterile neutrino mixing using atmospheric neutrinos in Super-Kamiokande, Phys. Rev. D 91, 052019 (2015).
- B. R. Smithers, B. J. P. Jones, C. A. Argüelles, J. M. Conrad, and A. Diaz, Cascade appearance signatures of sterile neutrinos at 1–100 TeV, Phys. Rev. D 105, 052001 (2022).
- C. A. Argüelles and J. Salvado, Sterile neutrinos with neutrino telescopes, Universe 7, 426 (2021).
- K. Goldhagen, M. Maltoni, S. E. Reichard, and T. Schwetz, Testing sterile neutrino mixing with present and future solar neutrino data, Eur. Phys. J. C 82, 116 (2022).
- W. Dekens, J. de Vries, and T. Tong, Sterile neutrinos with non-standard interactions in - and -decay experiments, J. High Energy Phys. 08 (2021) 128.
- H. B. Camara, R. G. Felipe, and F. R. Joaquim, Minimal inverse-seesaw mechanism with Abelian flavour symmetries, J. High Energy Phys. 05 (2021) 021.
- J. H. Seo, Z. Atif, C. D. Shin, and K. K. Joo, Search for reactor neutrino directionality using a LAB-based Gd-loaded liquid scintillation detector, Nucl. Instrum. Methods Phys. Res., Sect. A 969, 164001 (2020).
- D. I. Britton et al., Measurement of the neutrino branching ratio, Phys. Rev. Lett. 68, 3000 (1992).
- D. A. Bryman and R. Shrock, Improved constraints on sterile neutrinos in the MeV to GeV mass range, Phys. Rev. D 100, 053006 (2019).
- D. A. Bryman and R. Shrock, Constraints on sterile neutrinos in the MeV to GeV mass range, Phys. Rev. D 100, 073011 (2019).
- P. Rubin et al. (CLEO Collaboration), Search for rare and forbidden decays of charm and charmed-strange mesons to final states , Phys. Rev. D 82, 092007 (2010).
- O. Seon et al. (BELLE Collaboration), Search for lepton-number-violating decays, Phys. Rev. D 84, 071106 (2011).
- R. Aaij et al. (LHCb Collaboration), Search for Majorana neutrinos in decays, Phys. Rev. Lett. 112, 131802 (2014).
- M. Ablikim et al. (BESIII Collaboration), Search for heavy Majorana neutrino in lepton number violating decays of , Phys. Rev. D 99, 112002 (2019).
- A. Tumasyan et al. (CMS Collaboration), Search for long-lived heavy neutral leptons with displaced vertices in proton-proton collisions at , J. High Energy Phys. 07 (2022) 081.
- G. Aad et al. (ATLAS Collaboration), Search for heavy neutral leptons in decays of W bosons using a dilepton displaced vertex in pp collisions with the ATLAS detector, Phys. Rev. Lett. 131, 061803 (2023).
- K. Bondarenko, A. Boyarsky, M. Ovchynnikov, O. Ruchayskiy, and L. Shchutska, Probing new physics with displaced vertices: Muon tracker at CMS, Phys. Rev. D 100, 075015 (2019).
- A. Hayrapetyan et al. (CMS Collaboration), Search for long-lived heavy neutral leptons in proton-proton collision events with a lepton-jet pair associated with a secondary vertex at , J. High Energy Phys. 02 (2025) 036.
- J. C. Helo, M. Hirsch, and S. Kovalenko, Heavy neutrino searches at the LHC with displaced vertices, Phys. Rev. D 89, 073005 (2014). 93, 099902(E) (2016)].
- J. Liu, Z. Liu, L.-T. Wang, and X.-P. Wang, Seeking for sterile neutrinos with displaced leptons at the LHC, J. High Energy Phys. 07 (2019) 159.
- G. Aad et al. (ATLAS Collaboration), Search for heavy neutral leptons in decays of W bosons using leptonic and semi-leptonic displaced vertices in collisions with the ATLAS detector, J. High Energy Phys. 07 (2025) 196.
- G. Aad et al. (ATLAS Collaboration), Search for neutral long-lived particles that decay into displaced jets in the ATLAS calorimeter in association with leptons or jets using pp collisions at , J. High Energy Phys. 11 (2024) 036.
- K. A. Urquía-Calderón, Long-lived heavy neutral leptons at lepton colliders as a probe of left-right-symmetric models, Phys. Rev. D 109, 055002 (2024).
- G. Cottin, J. C. Helo, M. Hirsch, C. Peña, C. Wang, and S. Xie, Long-lived heavy neutral leptons with a displaced shower signature at CMS, J. High Energy Phys. 02 (2023) 011.
- H. Yang, B. Long, and C.-F. Qiao, Hunting for sterile neutrino with future collider signatures, Nucl. Phys. B1004, 116576 (2024).
- D. Neuffer, Multi-TeV muon colliders, AIP Conf. Proc. 156, 201 (1987).
- C. M. Ankenbrandt et al., Status of muon collider research and development and future plans, Phys. Rev. ST Accel. Beams 2, 081001 (1999).
- M. Boscolo, J.-P. Delahaye, and M. Palmer, The future prospects of muon colliders and neutrino factories, Rev. Accel. Sci. Techol. 10, 189 (2019).
- K. Long, D. Lucchesi, M. Palmer, N. Pastrone, D. Schulte, and V. Shiltsev, Muon colliders to expand frontiers of particle physics, Nat. Phys. 17, 289 (2021).
- K. M. Black et al., Muon collider forum report, J. Instrum. 19, T02015 (2024).
- C. Accettura et al., Towards a muon collider, Eur. Phys. J. C 83, 864 (2023); 84, 36(E) (2024).
- T. Li, H. Qin, C.-Y. Yao, and M. Yuan, Probing heavy triplet leptons of the type-III seesaw mechanism at future muon colliders, Phys. Rev. D 106, 035021 (2022).
- I. Chakraborty, H. Roy, and T. Srivastava, Searches for heavy neutrinos at multi-TeV muon collider: A resonant leptogenesis perspective, Eur. Phys. J. C 83, 280 (2023).
- K. Mękała, J. Reuter, and A. F. Żarnecki, Optimal search reach for heavy neutral leptons at a muon collider, Phys. Lett. B 841, 137945 (2023).
- T. H. Kwok, L. Li, T. Liu, and A. Rock, Searching for heavy neutral leptons at a future muon collider, Phys. Rev. D 110, 075009 (2024).
- P. Li, Z. Liu, and K.-F. Lyu, Heavy neutral leptons at muon colliders, J. High Energy Phys. 03 (2023) 231.
- T. Li, C.-Y. Yao, and M. Yuan, Searching for heavy neutral lepton and lepton number violation through VBS at high-energy muon colliders, J. High Energy Phys. 09 (2023) 131.
- R.-Y. He, J.-Q. Huang, J.-Y. Xu, F.-X. Yang, Z.-L. Han, and F.-L. Shao, Heavy neutral leptons in gauged at muon collider, Chin. Phys. C 48, 093102 (2024).
- Q. Bi, J. Guo, J. Liu, Y. Luo, and X.-P. Wang, Long-lived sterile neutrino searches at future muon colliders, Phys. Rev. D 111, 075001 (2025).
- M. Shaposhnikov and A. Y. Smirnov, Sterile neutrino dark matter, matter-antimatter separation, and the QCD phase transition, Phys. Rev. D 110, 063520 (2024).
- J. Ma, S. Jiang, and X.-F. Li, Impact of Q-balls formed by first-order phase transition on sterile neutrino dark matter, Eur. Phys. J. C 84, 1016 (2024).
- D. J. H. Chung and A. J. Long, Electroweak phase transition in the munuSSM, Phys. Rev. D 81, 123531 (2010).
- L. Bian and Y.-L. Tang, Thermally modified sterile neutrino portal dark matter and gravitational waves from phase transition: The Freeze-in case, J. High Energy Phys. 12 (2018) 006.
- P. Di Bari, D. Marfatia, and Y.-L. Zhou, Gravitational waves from neutrino mass and dark matter genesis, Phys. Rev. D 102, 095017 (2020).
- P. Borah, P. Ghosh, S. Roy, and A. K. Saha, Electroweak phase transition in a right-handed neutrino superfield extended NMSSM, J. High Energy Phys. 08 (2023) 029.
- W. Liu, K.-P. Xie, and Z. Yi, Testing leptogenesis at the LHC and future muon colliders: A scenario, Phys. Rev. D 105, 095034 (2022).
- W. Liu, A. Yang, and H. Sun, Shedding light on the electroweak phase transition from exotic Higgs boson decays at the lifetime frontiers, Phys. Rev. D 105, 115040 (2022).
- J. Liu, X.-P. Wang, and K.-P. Xie, Searching for lepton portal dark matter with colliders and gravitational waves, J. High Energy Phys. 06 (2021) 149.
- K.-P. Xie, Lepton-mediated electroweak baryogenesis, gravitational waves and the final state at the collider, J. High Energy Phys. 02 (2021) 090.
- F. F. Deppisch, S. Kulkarni, and W. Liu, Heavy neutrino production via at the lifetime frontier, Phys. Rev. D 100, 035005 (2019).
- A. Das, S. Mandal, T. Nomura, and S. Shil, Heavy Majorana neutrino pair production from at hadron and lepton colliders, Phys. Rev. D 105, 095031 (2022).
- M. Carena, Z. Liu, and Y. Wang, Electroweak phase transition with spontaneous -breaking, J. High Energy Phys. 08 (2020) 107.
- S. Jana, N. Okada, and D. Raut, Displaced vertex signature of type-I seesaw, Phys. Rev. D 98, 035023 (2018).
- I. Zurbano Fernandez et al., High-Luminosity Large Hadron Collider (HL-LHC): Technical design report, Report No. CERN-2020-010, 2020.
- O. Solovyanov (ATLAS Collaboration), ATLAS upgrades for high luminosity LHC, Proc. Sci. DIS2024 (2025) 278.
- T. R. Fernandez Perez Tomei (CMS Collaboration), CMS upgrades for the high-luminosity LHC era, Proc. Sci. LHCP2024 (2025) 189 [arXiv:2501.03412].
- J. A. Casas and A. Ibarra, Oscillating neutrinos and , Nucl. Phys. B618, 171 (2001).
- M. Aker et al. (Katrin Collaboration), Direct neutrino-mass measurement based on 259 days of KATRIN data, Science 388, 180 (2025).
- B. W. Lee, C. Quigg, and H. B. Thacker, Weak interactions at very high-energies: The role of the Higgs boson mass, Phys. Rev. D 16, 1519 (1977).
- M. Luscher and P. Weisz, Is there a strong interaction sector in the standard lattice Higgs model?, Phys. Lett. B 212, 472 (1988).
- G. M. Pruna and T. Robens, Higgs singlet extension parameter space in the light of the LHC discovery, Phys. Rev. D 88, 115012 (2013).
- S. Navas et al. (Particle Data Group), Review of particle physics, Phys. Rev. D 110, 030001 (2024).
- T. Robens and T. Stefaniak, Status of the Higgs singlet extension of the standard model after LHC run 1, Eur. Phys. J. C 75, 104 (2015).
- H. H. Patel and M. J. Ramsey-Musolf, Baryon washout, electroweak phase transition, and perturbation theory, J. High Energy Phys. 07 (2011) 029.
- M. Fairbairn and R. Hogan, Singlet fermionic dark matter and the electroweak phase transition, J. High Energy Phys. 09 (2013) 022.
- W. Liu and K.-P. Xie, Probing electroweak phase transition with multi-TeV muon colliders and gravitational waves, J. High Energy Phys. 04 (2021) 015.
- L. Bian, H.-K. Guo, Y. Wu, and R. Zhou, Gravitational wave and collider searches for electroweak symmetry breaking patterns, Phys. Rev. D 101, 035011 (2020).
- K. Harigaya and I. R. Wang, First-order electroweak phase transition and baryogenesis from a naturally light singlet scalar, arXiv:2207.02867.
- P. B. Arnold and O. Espinosa, The effective potential and first order phase transitions: Beyond leading-order, Phys. Rev. D 47, 3546 (1993); 50, 6662(E) (1994).
- R. R. Parwani, Resummation in a hot scalar field theory, Phys. Rev. D 45, 4695 (1992); 48, 5965(E) (1993).
- J. R. Espinosa, T. Konstandin, and F. Riva, Strong electroweak phase transitions in the standard model with a singlet, Nucl. Phys. B854, 592 (2012).
- S. Profumo, M. J. Ramsey-Musolf, and G. Shaughnessy, Singlet Higgs phenomenology and the electroweak phase transition, J. High Energy Phys. 08 (2007) 010.
- A. Ahriche, What is the criterion for a strong first order electroweak phase transition in singlet models?, Phys. Rev. D 75, 083522 (2007).
- C. L. Wainwright, CosmoTransitions: Computing cosmological phase transition temperatures and bubble profiles with multiple fields, Comput. Phys. Commun. 183, 2006 (2012).
- A. D. Linde, Decay of the false vacuum at finite temperature, Nucl. Phys. B216, 421 (1983); B223, 544(E) (1983).
- M. Quiros, Finite temperature field theory and phase transitions, in ICTP Summer School in High-Energy Physics and Cosmology (1999), pp. 187–259, arXiv:hep-ph/9901312.
- A. Kosowsky, M. S. Turner, and R. Watkins, Gravitational radiation from colliding vacuum bubbles, Phys. Rev. D 45, 4514 (1992).
- A. Kosowsky and M. S. Turner, Gravitational radiation from colliding vacuum bubbles: Envelope approximation to many bubble collisions, Phys. Rev. D 47, 4372 (1993).
- S. J. Huber and T. Konstandin, Gravitational wave production by collisions: More bubbles, J. Cosmol. Astropart. Phys. 09 (2008) 022.
- D. Bodeker and G. D. Moore, Can electroweak bubble walls run away?, J. Cosmol. Astropart. Phys. 05 (2009) 009.
- R. Jinno, S. Lee, H. Seong, and M. Takimoto, Gravitational waves from first-order phase transitions: Towards model separation by bubble nucleation rate, J. Cosmol. Astropart. Phys. 11 (2017) 050.
- M. Hindmarsh, S. J. Huber, K. Rummukainen, and D. J. Weir, Gravitational waves from the sound of a first order phase transition, Phys. Rev. Lett. 112, 041301 (2014).
- M. Hindmarsh, S. J. Huber, K. Rummukainen, and D. J. Weir, Numerical simulations of acoustically generated gravitational waves at a first order phase transition, Phys. Rev. D 92, 123009 (2015).
- J. R. Espinosa, T. Konstandin, J. M. No, and G. Servant, Energy budget of cosmological first-order phase transitions, J. Cosmol. Astropart. Phys. 06 (2010) 028.
- 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.
- P. Binetruy, A. Bohe, C. Caprini, and J.-F. Dufaux, Cosmological backgrounds of gravitational waves and eLISA/NGO: Phase transitions, cosmic strings and other sources, J. Cosmol. Astropart. Phys. 06 (2012) 027.
- H. Shibuya and T. Toma, Impact of first-order phase transitions on dark matter production in the scotogenic model, J. High Energy Phys. 11 (2022) 064.
- 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.
- A. Klein et al., Science with the space-based interferometer eLISA: Supermassive black hole binaries, Phys. Rev. D 93, 024003 (2016).
- H. Kudoh, A. Taruya, T. Hiramatsu, and Y. Himemoto, Detecting a gravitational-wave background with next-generation space interferometers, Phys. Rev. D 73, 064006 (2006).
- K. Yagi and N. Seto, Detector configuration of DECIGO/BBO and identification of cosmological neutron-star binaries, Phys. Rev. D 83, 044011 (2011); 95, 109901(E) (2017).
- J. Luo et al. (TianQin Collaboration), TianQin: A space-borne gravitational wave detector, Classical Quantum Gravity 33, 035010 (2016).
- X. Gong et al., Descope of the ALIA mission, J. Phys. Conf. Ser. 610, 012011 (2015).
- C. Caprini et al., Detecting gravitational waves from cosmological phase transitions with LISA: An update, J. Cosmol. Astropart. Phys. 03 (2020) 024.
- A. Hayrapetyan et al. (CMS Collaboration), Search for heavy neutral leptons in final states with electrons, muons, and hadronically decaying tau leptons in proton-proton collisions at , J. High Energy Phys. 06 (2024) 123.
- A. Tumasyan et al. (CMS Collaboration), Probing heavy Majorana neutrinos and the weinberg operator through vector boson fusion processes in proton-proton collisions at , Phys. Rev. Lett. 131, 011803 (2023).
- J. Alwall, R. Frederix, S. Frixione, V. Hirschi, F. Maltoni, O. Mattelaer, H. S. Shao, T. Stelzer, P. Torrielli, and M. Zaro, The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations, J. High Energy Phys. 07 (2014) 079.
- A. Alloul, N. D. Christensen, C. Degrande, C. Duhr, and B. Fuks, FeynRules 2.0—A complete toolbox for tree-level phenomenology, Comput. Phys. Commun. 185, 2250 (2014).
- T. Sjostrand, S. Mrenna, and P. Z. Skands, A brief introduction to PYTHIA 8.1, Comput. Phys. Commun. 178, 852 (2008).
- J. de Favereau, C. Delaere, P. Demin, A. Giammanco, V. Lemaître, A. Mertens, and M. Selvaggi (DELPHES 3 Collaboration), DELPHES 3, A modular framework for fast simulation of a generic collider experiment, J. High Energy Phys. 02 (2014) 057.
- J. J. Heinrich, Reconstruction of boosted and bosons from fat jets, Master’s thesis, Copenhagen University, 2014.
- Q.-H. Cao, J. Guo, J. Liu, Y. Luo, and X.-P. Wang, Long-lived searches of vectorlike lepton and its accompanying scalar at colliders, Phys. Rev. D 110, 015029 (2024).
- M. Aaboud et al. (ATLAS Collaboration), Search for long-lived, massive particles in events with displaced vertices and missing transverse momentum in collisions with the ATLAS detector, Phys. Rev. D 97, 052012 (2018).
- C.-W. Chiang, G. Cottin, A. Das, and S. Mandal, Displaced heavy neutrinos from decays at the LHC, J. High Energy Phys. 12 (2019) 070.
- G. Aad et al. (ATLAS Collaboration), Search for massive, long-lived particles using multitrack displaced vertices or displaced lepton pairs in pp collisions at with the ATLAS detector, Phys. Rev. D 92, 072004 (2015).
- J. Liu, Z. Liu, L.-T. Wang, and X.-P. Wang, Enhancing sensitivities to long-lived particles with high granularity calorimeters at the LHC, J. High Energy Phys. 11 (2020) 066.