- 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

Pseudo-Nambu-Goldstone boson Higgs models: Naturalness at a tipping point

Matthew McCullough1,*, Adriana Menkara2,†, and Ennio Salvioni3,‡

  • *Contact author: matthew.mccullough@cern.ch
  • †Contact author: adriana.menkara@desy.de
  • ‡Contact author: ennio.salvioni@cern.ch
PDF

Phys. Rev. D 112, 075016 – Published 6 October, 2025

DOI: https://doi.org/10.1103/s8bz-lh14

Abstract

In scenarios where the Higgs is viewed as a pseudo-Nambu-Goldstone boson, the question of naturalness finds itself, from a phenomenological perspective, at a tipping point between direct searches and precision. If, by the end of the High-Luminosity LHC operation, all experimental results were to remain consistent with the Standard Model, precision Higgs coupling measurements would begin to drive the naturalness tension. To illustrate this from a fresh perspective, we construct a maximally natural “kitchen sink” model, throwing into the mix three approaches to symmetry-based naturalness: supersymmetry, twin Higgs, and pseudo-Nambu-Goldstone boson Higgs models with a Gegenbauer potential. In other words, we build a “supersymmetric Gegenbauer’s twin” model. This model not only maximizes naturalness, at least from a technical perspective, but can also interpolate between all three ingredients smoothly, revealing the interplay between direct exploration and precision. Implications for FCC-ee and FCC-hh are discussed.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (31)

  1. Collider Reach, http://collider-reach.cern.ch.
  2. A. Glioti, R. Rattazzi, L. Ricci, and L. Vecchi, Exploring the flavor symmetry landscape, SciPost Phys. 18, 201 (2025).
  3. G. Panico and A. Wulzer, The composite Nambu-Goldstone higgs, Lect. Notes Phys. 913, 1 (2016).
  4. J. de Blas et al., Higgs boson studies at future particle colliders, J. High Energy Phys. 01 (2020) 139.
  5. A. Bernal, J. A. Casas, and J. M. Moreno, Fine-tuning in the 2HDM, Eur. Phys. J. C 82, 950 (2022).
  6. A. Djouadi, The anatomy of electro-weak symmetry breaking. II. The Higgs bosons in the minimal supersymmetric model, Phys. Rep. 459, 1 (2008).
  7. R. Davies, J. March-Russell, and M. McCullough, A supersymmetric one Higgs doublet model, J. High Energy Phys. 04 (2011) 108.
  8. G. F. Giudice, C. Grojean, A. Pomarol, and R. Rattazzi, The strongly-interacting light Higgs, J. High Energy Phys. 06 (2007) 045.
  9. ATLAS Collaboration, Combined measurements of Higgs boson production and decay using up to 139  fb−1 of proton-proton collision data at s=13  TeV collected with the ATLAS experiment, Report No. ATLAS-CONF-2021-053, 2021, https://cds.cern.ch/record/2789544.
  10. CMS Collaboration, Combined Higgs boson production and decay measurements with up to 137  fb−1 of pp collision data at s=13  TeV, Report No. CMS-PAS-HIG-19-005, 2020, https://cds.cern.ch/record/2706103.
  11. G. Durieux, M. McCullough, and E. Salvioni, Gegenbauer Goldstones, J. High Energy Phys. 01 (2022) 076.
  12. G. Durieux, M. McCullough, and E. Salvioni, Gegenbauer’s twin, J. High Energy Phys. 05 (2022) 140.
  13. K. Agashe, R. Contino, and A. Pomarol, The minimal composite Higgs model, Nucl. Phys. B719, 165 (2005).
  14. Z. Chacko, H.-S. Goh, and R. Harnik, The twin Higgs: Natural electroweak breaking from mirror symmetry, Phys. Rev. Lett. 96, 231802 (2006).
  15. R. Barbieri, T. Gregoire, and L. J. Hall, Mirror world at the Large Hadron Collider, arXiv:hep-ph/0509242.
  16. Z. Chacko, Y. Nomura, M. Papucci, and G. Perez, Natural little hierarchy from a partially Goldstone twin Higgs, J. High Energy Phys. 01 (2006) 126.
  17. Z. Chacko, H.-S. Goh, and R. Harnik, A twin Higgs model from left-right symmetry, J. High Energy Phys. 01 (2006) 108.
  18. R. Barbieri, D. Greco, R. Rattazzi, and A. Wulzer, The composite twin Higgs scenario, J. High Energy Phys. 08 (2015) 161.
  19. R. Contino, D. Greco, R. Mahbubani, R. Rattazzi, and R. Torre, Precision tests and fine tuning in twin Higgs models, Phys. Rev. D 96, 095036 (2017).
  20. M. Geller and O. Telem, Holographic twin Higgs model, Phys. Rev. Lett. 114, 191801 (2015).
  21. N. Craig, A. Katz, M. Strassler, and R. Sundrum, Naturalness in the dark at the LHC, J. High Energy Phys. 07 (2015) 105.
  22. M. Low, A. Tesi, and L.-T. Wang, Twin Higgs mechanism and a composite Higgs boson, Phys. Rev. D 91, 095012 (2015).
  23. A. Falkowski, S. Pokorski, and M. Schmaltz, Twin SUSY, Phys. Rev. D 74, 035003 (2006).
  24. S. Chang, L. J. Hall, and N. Weiner, A supersymmetric twin Higgs, Phys. Rev. D 75, 035009 (2007).
  25. N. Craig and K. Howe, Doubling down on naturalness with a supersymmetric twin Higgs, J. High Energy Phys. 03 (2014) 140.
  26. A. Katz, A. Mariotti, S. Pokorski, D. Redigolo, and R. Ziegler, SUSY meets her twin, J. High Energy Phys. 01 (2017) 142.
  27. M. Badziak and K. Harigaya, Supersymmetric D-term twin Higgs, J. High Energy Phys. 06 (2017) 065.
  28. M. Badziak and K. Harigaya, Minimal non-Abelian supersymmetric twin Higgs, J. High Energy Phys. 10 (2017) 109.
  29. M. Badziak and K. Harigaya, Asymptotically free natural supersymmetric twin Higgs model, Phys. Rev. Lett. 120, 211803 (2018).
  30. R. Barbieri and G. F. Giudice, Upper bounds on supersymmetric particle masses, Nucl. Phys. B306, 63 (1988).
  31. R. K. Ellis et al., Physics briefing book: Input for the European strategy for particle physics update 2020, arXiv:1910.11775.

Outline

Information

Phys. Rev. D 112, 075016– Published 6 October, 2025
  • Received 18 July 2025
  • Accepted 10 September 2025
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