- 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

Vacuum structure of the Babu-Nandi-Tavartkiladze model of neutrino mass generation

Saiyad Ashanujjaman1,2,* and Siddharth P. Maharathy3,4,†

  • *Contact author: saiyad.ashanujjaman@kit.edu
  • †Contact author: siddharth.prasad.maharathy@cern.ch
PDF

Phys. Rev. D 113, 075040 – Published 29 April, 2026

DOI: https://doi.org/10.1103/6hnd-rgch

Abstract

We analyze the vacuum structure of the Babu-Nandi-Tavartkiladze (BNT) model of neutrino mass generation, in which the Standard Model is extended by an SU(2)L scalar quadruplet with hypercharge Y=3/2 and a vectorlike SU(2)L triplet fermion with Y=1, generating neutrino masses via an effective dimension-seven operator. We delineate the theoretical constraints on the model, requiring the scalar potential to be bounded from below in all field directions, ensuring perturbative unitarity of scattering amplitudes, and demanding that the electroweak vacuum corresponds to the global minimum of the potential. We find that the electroweak vacuum is not generically guaranteed to be the global minimum: several charge-breaking stationary points may coexist with—and potentially lie below—it in potential depth. For the electroweak-like vacuum with vanishing quadruplet expectation value, the condition of global stability reduces to two simple mass inequalities involving the doubly and triply charged scalars. In contrast, for the general electroweak vacuum with nonzero doublet and quadruplet expectation values—compatible with neutrino-mass generation—no comparably simple analytic condition emerges, and the stability must in general be assessed for specific choices of scalar couplings. In the special case where the interaction responsible for neutrino-mass generation vanishes, both electroweak configurations coexist, and the bounded-from-below conditions ensure a definite ordering between them. In this limit, the mass inequalities alone are sufficient to guarantee that the general electroweak vacuum is the global minimum. In the physically relevant regime, the results provide practical sufficient criteria and a systematic framework for assessing vacuum stability in the BNT model.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (36)

  1. S. Weinberg, Baryon and lepton nonconserving processes, Phys. Rev. Lett. 43, 1566 (1979).
  2. E. Ma, Pathways to naturally small neutrino masses, Phys. Rev. Lett. 81, 1171 (1998).
  3. P. Minkowski, μ→eγ at a rate of one out of 109 muon decays?, Phys. Lett. B 67, 421 (1977).
  4. T. Yanagida, Horizontal gauge symmetry and masses of neutrinos, Conf. Proc. C 7902131, 95 (1979).
  5. M. Gell-Mann, P. Ramond, and R. Slansky, Complex spinors and unified theories, Conf. Proc. C 790927, 315 (1979).
  6. S. L. Glashow, The future of elementary particle physics, NATO Sci. Ser. B 61, 687 (1980).
  7. R. N. Mohapatra and G. Senjanovic, Neutrino mass and spontaneous parity nonconservation, Phys. Rev. Lett. 44, 912 (1980).
  8. 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).
  9. F. Bonnet, D. Hernandez, T. Ota, and W. Winter, Neutrino masses from higher than d=5 effective operators, J. High Energy Phys. 10 (2009) 076.
  10. S. Kanemura and T. Ota, Neutrino masses from loop-induced d≥7 operators, Phys. Lett. B 694, 233 (2011).
  11. Y. Liao, Unique neutrino mass operator at any mass dimension, Phys. Lett. B 694, 346 (2011).
  12. F. Bonnet, M. Hirsch, T. Ota, and W. Winter, Systematic study of the d=5 Weinberg operator at one-loop order, J. High Energy Phys. 07 (2012) 153.
  13. R. Cepedello, M. Hirsch, and J. C. Helo, Lepton number violating phenomenology of d=7 neutrino mass models, J. High Energy Phys. 01 (2017) 009.
  14. G. Anamiati, O. Castillo-Felisola, R. M. Fonseca, J. C. Helo, and M. Hirsch, High-dimensional neutrino masses, J. High Energy Phys. 12 (2018) 066.
  15. S. Ashanujjaman and K. Ghosh, A genuine fermionic quintuplet seesaw model: Phenomenological introduction, J. High Energy Phys. 06 (2020) 084.
  16. K. S. Babu, S. Nandi, and Z. Tavartkiladze, New mechanism for neutrino mass generation and triply charged Higgs bosons at the LHC, Phys. Rev. D 80, 071702 (2009).
  17. Y. Liao, G.-Z. Ning, and L. Ren, Flavor violating transitions of charged leptons from a seesaw mechanism of dimension seven, Phys. Rev. D 82, 113003 (2010).
  18. K. Ghosh, S. Jana, and S. Nandi, Neutrino mass generation and 750 GeV diphoton excess via photon-photon fusion at the large hadron collider, arXiv:1607.01910.
  19. G. Bambhaniya, J. Chakrabortty, S. Goswami, and P. Konar, Generation of neutrino mass from new physics at TeV scale and multilepton signatures at the LHC, Phys. Rev. D 88, 075006 (2013).
  20. K. S. Babu and S. Jana, Probing doubly charged Higgs bosons at the LHC through photon initiated processes, Phys. Rev. D 95, 055020 (2017).
  21. K. Ghosh, S. Jana, and S. Nandi, Neutrino mass generation at TeV scale and new physics signatures from charged Higgs at the LHC for photon initiated processes, J. High Energy Phys. 03 (2017) 180.
  22. T. Ghosh, S. Jana, and S. Nandi, Neutrino mass from Higgs quadruplet and multicharged Higgs searches at the LHC, Phys. Rev. D 97, 115037 (2018).
  23. J. Pan, J.-H. Chen, X.-G. He, G. Li, and J.-Y. Su, Triply charged Higgs bosons at a 100 TeV pp collider, Eur. Phys. J. C 81, 43 (2021).
  24. C. Arbeláez, J. C. Helo, and M. Hirsch, Long-lived heavy particles in neutrino mass models, Phys. Rev. D 100, 055001 (2019).
  25. S. Navas et al. (Particle Data Group), Review of particle physics, Phys. Rev. D 110, 030001 (2024).
  26. K. Hadeler, On copositive matrices, Linear Algebra Appl. 49, 79 (1983).
  27. G. Chang and T. W. Sederberg, Nonnegative quadratic bézier triangular patches, Comput. Aided Geom. Des. 11, 113 (1994).
  28. H. E. Logan, Lectures on perturbative unitarity and decoupling in Higgs physics, arXiv:2207.01064.
  29. P. B. Pal, What is the equivalence theorem really?, arXiv:hep-ph/9405362.
  30. J. Horejsi, Electroweak interactions and high-energy limit: An introduction to equivalence theorem, Czech. J. Phys. 47, 951 (1997).
  31. P. M. Ferreira, R. Santos, and A. Barroso, Stability of the tree-level vacuum in two Higgs doublet models against charge or CP spontaneous violation, Phys. Lett. B 603, 219 (2004); 629, 114(E) (2005).
  32. A. Barroso, P. M. Ferreira, and R. Santos, Charge and CP symmetry breaking in two Higgs doublet models, Phys. Lett. B 632, 684 (2006).
  33. K. Kannike, Vacuum stability conditions from copositivity criteria, Eur. Phys. J. C 72, 2093 (2012).
  34. P. M. Ferreira and B. L. Gonçalves, Stability of neutral minima against charge breaking in the Higgs triplet model, J. High Energy Phys. 02 (2019) 182.
  35. D. Azevedo, P. Ferreira, H. E. Logan, and R. Santos, Vacuum structure of the Z2 symmetric Georgi-Machacek model, J. High Energy Phys. 03 (2020) 221.
  36. R. S. Hundi, Study on the global minimum and H→γγ in the Dirac scotogenic model, Phys. Rev. D 108, 015006 (2023).

Outline

Information

Phys. Rev. D 113, 075040– Published 29 April, 2026
  • Received 23 December 2025
  • Accepted 10 April 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