Journal of High Energy Physics

, 2016:130 | Cite as

The spontaneous \( {\mathbb{Z}}_2 \) breaking Twin Higgs

  • Hugues Beauchesne
  • Kevin Earl
  • Thomas Grégoire
Open Access
Regular Article - Theoretical Physics


The Twin Higgs model seeks to address the little hierarchy problem by making the Higgs a pseudo-Goldstone of a global SU(4) symmetry that is spontaneously broken to SU(3). Gauge and Yukawa couplings, which explicitly break SU(4), enjoy a discrete \( {\mathbb{Z}}_2 \) symmetry that accidentally maintains SU(4) at the quadratic level and therefore keeps the Higgs light. Contrary to most beyond the Standard Model theories, the quadratically divergent corrections to the Higgs mass are cancelled by a mirror sector, which is uncharged under the Standard Model groups. However, the Twin Higgs with an exact \( {\mathbb{Z}}_2 \) symmetry leads to equal vevs in the Standard Model and mirror sectors, which is phenomenologically unviable. An explicit \( {\mathbb{Z}}_2 \) breaking potential must then be introduced and tuned against the SU(4) breaking terms to produce a hierarchy of vevs between the two sectors. This leads to a moderate but non-negligible tuning. We propose a model to alleviate this tuning, without the need for an explicit \( {\mathbb{Z}}_2 \) breaking sector. The model consists of two SU(4) fundamental Higgses, one whose vacuum preserves \( {\mathbb{Z}}_2 \) and one whose vacuum breaks it. As the interactions between the two Higgses are turned on, the \( {\mathbb{Z}}_2 \) breaking is transmitted from the broken to the unbroken sector and a small hierarchy of vevs is naturally produced. The presence of an effective tadpole and feedback between the two Higgses lead to a sizable improvement of the tuning. The resulting Higgs boson is naturally very Standard Model like.


Beyond Standard Model Global Symmetries Higgs Physics 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


  1. [1]
    R. Barbieri and A. Strumia, The ‘LEP paradox’, talk given at the 4th Rencontres du Vietnam: Physics at Extreme Energies (Particle Physics and Astrophysics), July 19-25, Hanoi, Vietnam (2000), hep-ph/0007265 [INSPIRE].
  2. [2]
    Z. Chacko, H.-S. Goh and R. Harnik, The Twin Higgs: natural electroweak breaking from mirror symmetry, Phys. Rev. Lett. 96 (2006) 231802 [hep-ph/0506256] [INSPIRE].
  3. [3]
    R. Barbieri, T. Gregoire and L.J. Hall, Mirror world at the large hadron collider, hep-ph/0509242 [INSPIRE].
  4. [4]
    G. Burdman, Z. Chacko, H.-S. Goh and R. Harnik, Folded supersymmetry and the LEP paradox, JHEP 02 (2007) 009 [hep-ph/0609152] [INSPIRE].
  5. [5]
    H. Cai, H.-C. Cheng and J. Terning, A quirky little Higgs model, JHEP 05 (2009) 045 [arXiv:0812.0843] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  6. [6]
    G. Burdman, Z. Chacko, H.-S. Goh, R. Harnik and C.A. Krenke, The quirky collider signals of folded supersymmetry, Phys. Rev. D 78 (2008) 075028 [arXiv:0805.4667] [INSPIRE].ADSGoogle Scholar
  7. [7]
    D. Poland and J. Thaler, The dark top, JHEP 11 (2008) 083 [arXiv:0808.1290] [INSPIRE].CrossRefADSGoogle Scholar
  8. [8]
    P. Batra and Z. Chacko, A composite Twin Higgs model, Phys. Rev. D 79 (2009) 095012 [arXiv:0811.0394] [INSPIRE].ADSGoogle Scholar
  9. [9]
    N. Craig, S. Knapen and P. Longhi, Neutral naturalness from orbifold Higgs models, Phys. Rev. Lett. 114 (2015) 061803 [arXiv:1410.6808] [INSPIRE].CrossRefADSGoogle Scholar
  10. [10]
    N. Craig, S. Knapen and P. Longhi, The orbifold Higgs, JHEP 03 (2015) 106 [arXiv:1411.7393] [INSPIRE].CrossRefMathSciNetGoogle Scholar
  11. [11]
    G. Burdman, Z. Chacko, R. Harnik, L. de Lima and C.B. Verhaaren, Colorless top partners, a 125 GeV Higgs and the limits on naturalness, Phys. Rev. D 91 (2015) 055007 [arXiv:1411.3310] [INSPIRE].ADSGoogle Scholar
  12. [12]
    R. Barbieri, D. Greco, R. Rattazzi and A. Wulzer, The composite Twin Higgs scenario, JHEP 08 (2015) 161 [arXiv:1501.07803] [INSPIRE].CrossRefMathSciNetGoogle Scholar
  13. [13]
    M. Low, A. Tesi and L.-T. Wang, Twin Higgs mechanism and a composite Higgs boson, Phys. Rev. D 91 (2015) 095012 [arXiv:1501.07890] [INSPIRE].ADSGoogle Scholar
  14. [14]
    I. García García, R. Lasenby and J. March-Russell, Twin Higgs WIMP dark matter, Phys. Rev. D 92 (2015) 055034 [arXiv:1505.07109] [INSPIRE].ADSGoogle Scholar
  15. [15]
    N. Craig and A. Katz, The Fraternal WIMP Miracle, JCAP 10 (2015) 054 [arXiv:1505.07113] [INSPIRE].CrossRefADSGoogle Scholar
  16. [16]
    I. García García, R. Lasenby and J. March-Russell, Twin Higgs asymmetric dark matter, Phys. Rev. Lett. 115 (2015) 121801 [arXiv:1505.07410] [INSPIRE].CrossRefADSGoogle Scholar
  17. [17]
    M. Farina, Asymmetric twin dark matter, JCAP 11 (2015) 017 [arXiv:1506.03520] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  18. [18]
    B. Batell and M. McCullough, Neutrino masses from neutral top partners, Phys. Rev. D 92 (2015) 073018 [arXiv:1504.04016] [INSPIRE].
  19. [19]
    N. Craig, A. Katz, M. Strassler and R. Sundrum, Naturalness in the dark at the LHC, JHEP 07 (2015) 105 [arXiv:1501.05310] [INSPIRE].CrossRefADSGoogle Scholar
  20. [20]
    D. Curtin and C.B. Verhaaren, Discovering uncolored naturalness in exotic Higgs decays, JHEP 12 (2015) 072 [arXiv:1506.06141] [INSPIRE].CrossRefADSGoogle Scholar
  21. [21]
    D. Curtin and P. Saraswat, Towards a no-lose theorem for naturalness, arXiv:1509.04284 [INSPIRE].
  22. [22]
    Z. Chacko, Y. Nomura, M. Papucci and G. Perez, Natural little hierarchy from a partially Goldstone twin Higgs, JHEP 01 (2006) 126 [hep-ph/0510273] [INSPIRE].
  23. [23]
    S. Chang, L.J. Hall and N. Weiner, A supersymmetric twin Higgs, Phys. Rev. D 75 (2007) 035009 [hep-ph/0604076] [INSPIRE].
  24. [24]
    P.J. Fox, A.E. Nelson and N. Weiner, Dirac gaugino masses and supersoft supersymmetry breaking, JHEP 08 (2002) 035 [hep-ph/0206096] [INSPIRE].
  25. [25]
    A. Falkowski, S. Pokorski and M. Schmaltz, Twin SUSY, Phys. Rev. D 74 (2006) 035003 [hep-ph/0604066] [INSPIRE].
  26. [26]
    J. Galloway, M.A. Luty, Y. Tsai and Y. Zhao, Induced electroweak symmetry breaking and supersymmetric naturalness, Phys. Rev. D 89 (2014) 075003 [arXiv:1306.6354] [INSPIRE].ADSGoogle Scholar
  27. [27]
    N. Craig and K. Howe, Doubling down on naturalness with a supersymmetric twin Higgs, JHEP 03 (2014) 140 [arXiv:1312.1341] [INSPIRE].CrossRefADSGoogle Scholar
  28. [28]
    Particle Data Group collaboration, K.A. Olive et al., Review of particle physics, Chin. Phys. C 38 (2014) 090001 [INSPIRE].
  29. [29]
    ATLAS, CMS collaboration, Combined measurement of the Higgs boson mass in pp collisions at \( \sqrt{s}=7 \) and 8 TeV with the ATLAS and CMS experiments, Phys. Rev. Lett. 114 (2015) 191803 [arXiv:1503.07589] [INSPIRE].

Copyright information

© The Author(s) 2016

Authors and Affiliations

  • Hugues Beauchesne
    • 1
  • Kevin Earl
    • 1
  • Thomas Grégoire
    • 1
  1. 1.Ottawa-Carleton Institute for Physics, Department of PhysicsCarleton UniversityOttawaCanada

Personalised recommendations