Abstract
We catalogue and study three-Higgs-doublet models in terms of all possible allowed symmetries (continuous and discrete, Abelian and non-Abelian), where such symmetries may be identified as flavour symmetries of quarks and leptons. We analyse the potential in each case, and derive the conditions under which the vacuum alignments (0, 0, v), (0, v, v) and (v, v, v) are minima of the potential. For the alignment (0, 0, v), relevant for dark matter models, we calculate the corresponding physical Higgs boson mass spectrum. Motivated by supersymmetry, we extend the analysis to the case of three up-type Higgs doublets and three down-type Higgs doublets (six doublets in total). Many of the results are also applicable to flavon models where the three Higgs doublets are replaced by three electroweak singlets.
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References
ATLAS collaboration, Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC, Phys. Lett. B 716 (2012) 1 [arXiv:1207.7214] [INSPIRE].
CMS collaboration, Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC, Phys. Lett. B 716 (2012) 30 [arXiv:1207.7235] [INSPIRE].
J.F. Gunion, H.E. Haber, G.L. Kane and S. Dawson, The Higgs hunter’s guide, Front. Phys. 80 (2000) 1 [INSPIRE].
D. Chung et al., The soft supersymmetry breaking Lagrangian: theory and applications, Phys. Rept. 407 (2005) 1 [hep-ph/0312378] [INSPIRE].
S. Chang et al., Two Higgs doublet models for the LHC Higgs boson data at \( \sqrt{s} \) = 7 and 8 TeV, arXiv:1310.3374 [INSPIRE].
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].
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].
C. Nishi, Physical parameters and basis transformations in the two-Higgs-doublet model, Phys. Rev. D 77 (2008) 055009 [arXiv:0712.4260] [INSPIRE].
I.P. Ivanov, Minkowski space structure of the Higgs potential in 2HDM. II. Minima, symmetries and topology, Phys. Rev. D 77 (2008) 015017 [arXiv:0710.3490] [INSPIRE].
R.A. Battye, G.D. Brawn and A. Pilaftsis, Vacuum topology of the two Higgs doublet model, JHEP 08 (2011) 020 [arXiv:1106.3482] [INSPIRE].
A. Pilaftsis, On the classification of accidental symmetries of the two Higgs doublet model potential, Phys. Lett. B 706 (2012) 465 [arXiv:1109.3787] [INSPIRE].
I.P. Ivanov, V. Keus and E. Vdovin, Abelian symmetries in multi-Higgs-doublet models, J. Phys. A 45 (2012) 215201 [arXiv:1112.1660] [INSPIRE].
I. Ivanov and C. Nishi, Properties of the general NHDM. I. The orbit space, Phys. Rev. D 82 (2010) 015014 [arXiv:1004.1799] [INSPIRE].
I. Ivanov, Properties of the general NHDM. II. Higgs potential and its symmetries, JHEP 07 (2010) 020 [arXiv:1004.1802] [INSPIRE].
R. Mohapatra and C. Nishi, Absence of spontaneous CP-violation in multi-Higgs doublet extension of MSSM, Phys. Rev. D 84 (2011) 095023 [arXiv:1108.1769] [INSPIRE].
I.P. Ivanov and V. Keus, Frustrated symmetries in multi-Higgs-doublet models, Phys. Lett. B 695 (2011) 459 [arXiv:1007.5305] [INSPIRE].
I. Ivanov and V. Keus, Z p scalar dark matter from multi-Higgs-doublet models, Phys. Rev. D 86 (2012) 016004 [arXiv:1203.3426] [INSPIRE].
I. Ivanov and E. Vdovin, Classification of finite reparametrization symmetry groups in the three-Higgs-doublet model, Eur. Phys. J. C 73 (2013) 2309 [arXiv:1210.6553] [INSPIRE].
R. González Felipe, H. Serôdio and J.P. Silva, Models with three Higgs doublets in the triplet representations of A 4 or S 4, Phys. Rev. D 87 (2013) 055010 [arXiv:1302.0861] [INSPIRE].
S. Morisi, E. Peinado, Y. Shimizu and J. Valle, Relating quarks and leptons without grand-unification, Phys. Rev. D 84 (2011) 036003 [arXiv:1104.1633] [INSPIRE].
S. King, S. Moretti and R. Nevzorov, Theory and phenomenology of an exceptional supersymmetric Standard Model, Phys. Rev. D 73 (2006) 035009 [hep-ph/0510419] [INSPIRE].
S. King, S. Moretti and R. Nevzorov, Exceptional supersymmetric Standard Model, Phys. Lett. B 634 (2006) 278 [hep-ph/0511256] [INSPIRE].
R. Howl and S. King, Solving the flavour problem in supersymmetric Standard Models with three Higgs families, Phys. Lett. B 687 (2010) 355 [arXiv:0908.2067] [INSPIRE].
A. Degee, I. Ivanov and V. Keus, Geometric minimization of highly symmetric potentials, JHEP 02 (2013) 125 [arXiv:1211.4989] [INSPIRE].
J. Unwin, Vacuum stability and the Cholesky decomposition, Eur. Phys. J. C 71 (2011) 1663 [arXiv:1102.2896] [INSPIRE].
B. Grzadkowski, O. Ogreid, P. Osland, A. Pukhov and M. Purmohammadi, Exploring the CP-violating inert-doublet model, JHEP 06 (2011) 003 [arXiv:1012.4680] [INSPIRE].
H. Ishimori et al., Non-Abelian discrete symmetries in particle physics, Prog. Theor. Phys. Suppl. 183 (2010) 1 [arXiv:1003.3552] [INSPIRE].
L. Lavoura and J.P. Silva, Fundamental CP-violating quantities in a SU(2) × U(1) model with many Higgs doublets, Phys. Rev. D 50 (1994) 4619 [hep-ph/9404276] [INSPIRE].
F. Botella and J.P. Silva, Jarlskog-like invariants for theories with scalars and fermions, Phys. Rev. D 51 (1995) 3870 [hep-ph/9411288] [INSPIRE].
G.C. Branco, L. Lavoura and J.P. Silva, CP violation, Int. Ser. Monogr. Phys. 103 (1999) 1 [INSPIRE].
C. Nishi, CP violation conditions in N -Higgs-doublet potentials, Phys. Rev. D 74 (2006) 036003 [Erratum ibid. D 76 (2007) 119901] [hep-ph/0605153] [INSPIRE].
P. Ferreira, H.E. Haber, M. Maniatis, O. Nachtmann and J.P. Silva, Geometric picture of generalized-CP and Higgs-family transformations in the two-Higgs-doublet model, Int. J. Mod. Phys. A 26 (2011) 769 [arXiv:1010.0935] [INSPIRE].
I. Ivanov, Two-Higgs-doublet model from the group-theoretic perspective, Phys. Lett. B 632 (2006) 360 [hep-ph/0507132] [INSPIRE].
I. Ivanov, Minkowski space structure of the Higgs potential in 2HDM, Phys. Rev. D 75 (2007) 035001 [Erratum ibid. D 76 (2007) 039902] [hep-ph/0609018] [INSPIRE].
I.P. Ivanov, Minkowski space structure of the Higgs potential in 2HDM. II. Minima, symmetries and topology, Phys. Rev. D 77 (2008) 015017 [arXiv:0710.3490] [INSPIRE].
G. Sartori and G. Valente, Allowed and observable phases in two Higgs doublet Standard Models, Ph.D. thesis, http://www.ub.uni-heidelberg.de/archiv/4803, University Heidelberg, Heidelberg Germany (2004) [hep-ph/0304026] [INSPIRE].
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].
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Keus, V., King, S.F. & Moretti, S. Three-Higgs-doublet models: symmetries, potentials and Higgs boson masses. J. High Energ. Phys. 2014, 52 (2014). https://doi.org/10.1007/JHEP01(2014)052
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DOI: https://doi.org/10.1007/JHEP01(2014)052