Journal of High Energy Physics

, 2011:30 | Cite as

The bilinear formalism and the custodial symmetry in the two-Higgs-doublet model

Open Access

A bstract

We present a simple and transparent analysis of custodial symmetry in the Two-Higgs-Doublet Model adopting the bilinear formalism for the Higgs potential. The method allows to derive basis-independent, necessary and sufficient conditions for the potential to be invariant under custodial transformations. The relation between the custodial transformation and CP is revisited and clarified.

K eywords

Beyond Standard Model Discrete and Finite Symmetries 


  1. [1]
    Particle DataGroup collaboration, K. Nakamura et al., Review of particle physics, J. Phys. G 37 (2010) 075021 [INSPIRE]ADSGoogle Scholar
  2. [2]
    P. Sikivie, L. Susskind, M.B. Voloshin and V.I. Zakharov, Isospin breaking in technicolor models, Nucl. Phys. B 173 (1980) 189 [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    M.E. Peskin and D.V. Schroeder, An introduction to quantum field theory, Addison-Wesley, Reading U.S.A. (1995) [INSPIRE].
  4. [4]
    D. Toussaint, Renormalization effects from superheavy Higgs particles, Phys. Rev. D 18 (1978) 1626 [INSPIRE].ADSGoogle Scholar
  5. [5]
    R. Lytel, Weak isospin breaking and higher order corrections, Phys. Rev. D 22 (1980) 505 [INSPIRE].ADSGoogle Scholar
  6. [6]
    A. Pomarol and R. Vega, Constraints on CP-violation in the Higgs sector from the ρ parameter, Nucl. Phys. B 413 (1994) 3 [hep-ph/9305272] [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    R. Barbieri, L.J. Hall and V.S. Rychkov, Improved naturalness with a heavy Higgs: an alternative road to LHC physics, Phys. Rev. D 74 (2006) 015007 [hep-ph/0603188] [INSPIRE].ADSGoogle Scholar
  8. [8]
    F. Nagel, New aspects of gauge-boson couplings and the Higgs sector, Ph.D. thesis, Fakultät für Physik und Astronomie, Institut für Theoretische Physik, Ruperto-Carola University of Heidelberg, Heidelberg Germany (2004) [INSPIRE].
  9. [9]
    M. Maniatis, A. von Manteuffel, O. Nachtmann and F. Nagel, Stability and symmetry breaking in the general two-Higgs-doublet model, Eur. Phys. J. C 48 (2006) 805 [hep-ph/0605184] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    S. Davidson and H.E. Haber, Basis-independent methods for the two-Higgs-doublet model, Phys. Rev. D 72 (2005) 035004 [Erratum ibid. D 72 (2005) 099902] [hep-ph/0504050] [INSPIRE].ADSGoogle Scholar
  11. [11]
    H.E. Haber and D. O’Neil, Basis-independent methods for the two-Higgs-doublet model. II. The significance of tan β, Phys. Rev. D 74 (2006) 015018 [hep-ph/0602242] [INSPIRE]ADSGoogle Scholar
  12. [12]
    C. Nishi, Physical parameters and basis transformations in the two-Higgs-doublet model, Phys. Rev. D 77 (2008) 055009 [arXiv:0712.4260] [INSPIRE].ADSGoogle Scholar
  13. [13]
    P. Ferreira, H.E. Haber and J.P. Silva, Basis invariant conditions for supersymmetry in the two-Higgs-doublet model, Phys. Rev. D 82 (2010) 016001 [arXiv:1004.3292] [INSPIRE].ADSGoogle Scholar
  14. [14]
    H.E. Haber and D. O’Neil, Basis-independent methods for the two-Higgs-doublet model III: the CP-conserving limit, custodial symmetry and the oblique parameters S, T, U, Phys. Rev. D 83 (2011) 055017 [arXiv:1011.6188] [INSPIRE].ADSGoogle Scholar
  15. [15]
    H.E. Haber and R. Hempfling, The renormalization group improved Higgs sector of the minimal supersymmetric model, Phys. Rev. D 48 (1993) 4280 [hep-ph/9307201] [INSPIRE].ADSGoogle Scholar
  16. [16]
    M. Maniatis, A. von Manteuffel and O. Nachtmann, CP violation in the general two-Higgs-doublet model: a geometric view, Eur. Phys. J. C 57 (2008) 719 [arXiv:0707.3344] [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    H.-J. He, N. Polonsky and S.-F. Su, Extra families, Higgs spectrum and oblique corrections, Phys. Rev. D 64 (2001) 053004 [hep-ph/0102144] [INSPIRE].ADSGoogle Scholar
  18. [18]
    C. Nishi, Custodial SO(4) symmetry and CP-violation in N-Higgs-doublet potentials, Phys. Rev. D 83 (2011) 095005 [arXiv:1103.0252] [INSPIRE].ADSGoogle Scholar
  19. [19]
    K. Olaussen, P. Osland and M. Solberg, Symmetry and mass degeneration in multi-Higgs-doublet models, JHEP 07 (2011) 020 [arXiv:1007.1424] [INSPIRE].ADSCrossRefGoogle Scholar

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© The Author(s) 2011

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

Authors and Affiliations

  1. 1.Institute of Theoretical PhysicsUniversity of WarsawWarsawPoland
  2. 2.Institute for Theoretical PhysicsUniversity of BielefeldBielefeldGermany
  3. 3.Department of PhysicsUniversity of CaliforniaRiversideUSA

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