Abstract
A model with three scalar doublets can be conveniently accommodated within an A4 symmetric framework. The A4 symmetry permits only a restricted form for the scalar potential. We show that for the global minima of this potential alignment follows as a natural consequence. We also verify that in every case positivity and unitarity constraints are satisfactorily met.
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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].
A. Datta and A. Raychaudhuri, Next-to-minimal Higgs: mass bounds and search prospects, Phys. Rev. D 57 (1998) 2940 [hep-ph/9708444] [INSPIRE].
M. Magg and C. Wetterich, Neutrino mass problem and gauge hierarchy, Phys. Lett. B 94 (1980) 61 [INSPIRE].
G.C. Branco, P.M. Ferreira, L. Lavoura, M.N. Rebelo, M. Sher and J.P. Silva, Theory and phenomenology of two-Higgs-doublet models, Phys. Rept. 516 (2012) 1 [arXiv:1106.0034] [INSPIRE].
I.P. Ivanov, Building and testing models with extended Higgs sectors, Prog. Part. Nucl. Phys. 95 (2017) 160 [arXiv:1702.03776] [INSPIRE].
A. Pilaftsis, Symmetries for Standard Model alignment in multi-Higgs doublet models, Phys. Rev. D 93 (2016) 075012 [arXiv:1602.02017] [INSPIRE].
M.P. Bento, H.E. Haber, J.C. Romão and J.P. Silva, Multi-Higgs doublet models: physical parametrization, sum rules and unitarity bounds, JHEP 11 (2017) 095 [arXiv:1708.09408] [INSPIRE].
I.P. Ivanov and C.C. Nishi, Symmetry breaking patterns in 3HDM, JHEP 01 (2015) 021 [arXiv:1410.6139] [INSPIRE].
A. Aranda, C. Bonilla and J.L. Diaz-Cruz, Three generations of Higgses and the cyclic groups, Phys. Lett. B 717 (2012) 248 [arXiv:1204.5558] [INSPIRE].
A. Tofighi and M. Moazzen, Neutral minima in three-Higgs doublet models, Int. J. Theor. Phys. 48 (2009) 3372 [INSPIRE].
V. Keus, S.F. King and S. Moretti, Three-Higgs-doublet models: symmetries, potentials and Higgs boson masses, JHEP 01 (2014) 052 [arXiv:1310.8253] [INSPIRE].
I. de Medeiros Varzielas, S.F. King, C. Luhn and T. Neder, Minima of multi-Higgs potentials with triplets of Δ(3n 2) and Δ(6n 2), Phys. Lett. B 775 (2017) 303 [arXiv:1704.06322] [INSPIRE].
I. de Medeiros Varzielas, S.F. King, C. Luhn and T. Neder, Spontaneous CP-violation in multi-Higgs potentials with triplets of Δ(3n 2) and Δ(6n 2), JHEP 11 (2017) 136 [arXiv:1706.07606] [INSPIRE].
G. Bhattacharyya, P. Leser and H. Pas, Exotic Higgs boson decay modes as a harbinger of S 3 flavor symmetry, Phys. Rev. D 83 (2011) 011701 [arXiv:1006.5597] [INSPIRE].
D. Das and U.K. Dey, Analysis of an extended scalar sector with S 3 symmetry, Phys. Rev. D 89 (2014) 095025 [Erratum ibid. D 91 (2015) 039905] [arXiv:1404.2491] [INSPIRE].
N. Chakrabarty, High-scale validity of a model with three-Higgs-doublets, Phys. Rev. D 93 (2016) 075025 [arXiv:1511.08137] [INSPIRE].
E. Ma and G. Rajasekaran, Softly broken A 4 symmetry for nearly degenerate neutrino masses, Phys. Rev. D 64 (2001) 113012 [hep-ph/0106291] [INSPIRE].
R. de Adelhart Toorop, F. Bazzocchi, L. Merlo and A. Paris, Constraining flavour symmetries at the EW scale I: the A 4 Higgs potential, JHEP 03 (2011) 035 [Erratum ibid. 01 (2013) 098] [arXiv:1012.1791] [INSPIRE].
A.C.B. Machado, J.C. Montero and V. Pleitez, Three-Higgs-doublet model with A 4 symmetry, Phys. Lett. B 697 (2011) 318 [arXiv:1011.5855] [INSPIRE].
I. de Medeiros Varzielas, O. Fischer and V. Maurer, A 4 symmetry at colliders and in the universe, JHEP 08 (2015) 080 [arXiv:1504.03955] [INSPIRE].
H.E. Haber, Future Higgs studies: a theorist’s outlook, PoS(CHARGED2016)029, (2017) [arXiv:1701.01922] [INSPIRE].
G. Altarelli, Lectures on models of neutrino masses and mixings, arXiv:0711.0161 [INSPIRE].
H. Ishimori, T. Kobayashi, H. Ohki, Y. Shimizu, H. Okada and M. Tanimoto, Non-Abelian discrete symmetries in particle physics, Prog. Theor. Phys. Suppl. 183 (2010) 1 [arXiv:1003.3552] [INSPIRE].
S. Pramanick and A. Raychaudhuri, A4-based seesaw model for realistic neutrino masses and mixing, Phys. Rev. D 93 (2016) 033007 [arXiv:1508.02330] [INSPIRE].
S.F. King and C. Luhn, Neutrino mass and mixing with discrete symmetry, Rept. Prog. Phys. 76 (2013) 056201 [arXiv:1301.1340] [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.F. King and M. Malinsky, A 4 family symmetry and quark-lepton unification, Phys. Lett. B 645 (2007) 351 [hep-ph/0610250] [INSPIRE].
E. Ma, H. Sawanaka and M. Tanimoto, Quark masses and mixing with A 4 family symmetry, Phys. Lett. B 641 (2006) 301 [hep-ph/0606103] [INSPIRE].
S. Morisi, M. Nebot, K.M. Patel, E. Peinado and J.W.F. Valle, Quark-lepton mass relation and CKM mixing in an A 4 extension of the minimal supersymmetric Standard Model, Phys. Rev. D 88 (2013) 036001 [arXiv:1303.4394] [INSPIRE].
S. Morisi, E. Peinado, Y. Shimizu and J.W.F. Valle, Relating quarks and leptons without grand-unification, Phys. Rev. D 84 (2011) 036003 [arXiv:1104.1633] [INSPIRE].
A. Degee, I.P. Ivanov and V. Keus, Geometric minimization of highly symmetric potentials, JHEP 02 (2013) 125 [arXiv:1211.4989] [INSPIRE].
R. González Felipe, H. Serôdio and J.P. Silva, Neutrino masses and mixing in A 4 models with three Higgs doublets, Phys. Rev. D 88 (2013) 015015 [arXiv:1304.3468] [INSPIRE].
K. Kannike, Vacuum stability of a general scalar potential of a few fields, Eur. Phys. J. C 76 (2016) 324 [arXiv:1603.02680] [INSPIRE].
J. Chakrabortty, P. Konar and T. Mondal, Copositive criteria and boundedness of the scalar potential, Phys. Rev. D 89 (2014) 095008 [arXiv:1311.5666] [INSPIRE].
I.F. Ginzburg and I.P. Ivanov, Tree-level unitarity constraints in the most general 2HDM, Phys. Rev. D 72 (2005) 115010 [hep-ph/0508020] [INSPIRE].
S. Moretti and K. Yagyu, Constraints on parameter space from perturbative unitarity in models with three scalar doublets, Phys. Rev. D 91 (2015) 055022 [arXiv:1501.06544] [INSPIRE].
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Pramanick, S., Raychaudhuri, A. Three-Higgs-doublet model under A4 symmetry implies alignment. J. High Energ. Phys. 2018, 11 (2018). https://doi.org/10.1007/JHEP01(2018)011
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DOI: https://doi.org/10.1007/JHEP01(2018)011