Abstract
We analyze the compatibility between abelian symmetries acting in two different sectors of a theory using the Smith Normal Form method. We focus on N-Higgs-doublet models (NHDMs) and on the compatibility between symmetries in the Higgs potential and in the Yukawa interactions, which were separately analyzed in previous works. It is shown that two equal (isomorphic) symmetry groups that act in two separate sectors are not necessarily compatible in the whole theory and an upper bound is found for the size of the group that can be implemented in the entire NHDM. We also develop useful techniques to analyze compatibility and extend a symmetry from one sector to another. Consequences to the supersymmetric case are briefly discussed.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
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].
R.N. Mohapatra, From old symmetries to new symmetries: quarks, leptons and B-L, Int. J. Mod. Phys. A 29 (2014) 1430066 [arXiv:1409.7557] [INSPIRE].
G. Altarelli and F. Feruglio, Discrete flavor symmetries and models of neutrino mixing, Rev. Mod. Phys. 82 (2010) 2701 [arXiv:1002.0211] [INSPIRE].
H. Ishimori et al., Non-abelian discrete symmetries in particle physics, Prog. Theor. Phys. Suppl. 183 (2010) 1 [arXiv:1003.3552] [INSPIRE].
S.F. King and C. Luhn, Neutrino mass and mixing with discrete symmetry, Rept. Prog. Phys. 76 (2013) 056201 [arXiv:1301.1340] [INSPIRE].
S. Morisi and J.W.F. Valle, Neutrino masses and mixing: a flavour symmetry roadmap, Fortsch. Phys. 61 (2013) 466 [arXiv:1206.6678] [INSPIRE].
A.Y. Smirnov, Neutrino mass, mixing and discrete symmetries, J. Phys. Conf. Ser. 447 (2013) 012004 [arXiv:1305.4827] [INSPIRE].
G.R. Farrar and P. Fayet, Phenomenology of the production, decay and detection of new hadronic states associated with supersymmetry, Phys. Lett. B 76 (1978) 575 [INSPIRE].
S. Dimopoulos, S. Raby and F. Wilczek, Proton decay in supersymmetric models, Phys. Lett. B 112 (1982) 133 [INSPIRE].
B. Petersen, M. Ratz and R. Schieren, Patterns of remnant discrete symmetries, JHEP 08 (2009) 111 [arXiv:0907.4049] [INSPIRE].
R. Schieren, Discrete symmetries in the MSSM, arXiv:1102.4611 [INSPIRE].
M.-C. Chen, M. Ratz and V. Takhistov, R parity violation from discrete R symmetries, Nucl. Phys. B 891 (2015) 322 [arXiv:1410.3474] [INSPIRE].
R. González Felipe and H. Serôdio, Abelian realization of phenomenological two-zero neutrino textures, Nucl. Phys. B 886 (2014) 75 [arXiv:1405.4263] [INSPIRE].
I.P. Ivanov and C.C. Nishi, Abelian symmetries of the N-Higgs-doublet model with Yukawa interactions, JHEP 11 (2013) 069 [arXiv:1309.3682] [INSPIRE].
T.D. Lee, A theory of spontaneous T violation, Phys. Rev. D 8 (1973) 1226 [INSPIRE].
S. Weinberg, Gauge theory of CP-violation, Phys. Rev. Lett. 37 (1976) 657 [INSPIRE].
G.C. Branco, J.M. Gerard and W. Grimus, Geometrical T violation, Phys. Lett. B 136 (1984) 383 [INSPIRE].
I. de Medeiros Varzielas and D. Emmanuel-Costa, Geometrical CP-violation, Phys. Rev. D 84 (2011) 117901 [arXiv:1106.5477] [INSPIRE].
I. de Medeiros Varzielas, Geometrical CP-violation in multi-Higgs models, JHEP 08 (2012) 055 [arXiv:1205.3780] [INSPIRE].
I.P. Ivanov and L. Lavoura, Geometrical CP-violation in the N-Higgs-doublet model, Eur. Phys. J. C 73 (2013) 2416 [arXiv:1302.3656] [INSPIRE].
S.L. Glashow and S. Weinberg, Natural conservation laws for neutral currents, Phys. Rev. D 15 (1977) 1958 [INSPIRE].
E. Ma, Verifiable radiative seesaw mechanism of neutrino mass and dark matter, Phys. Rev. D 73 (2006) 077301 [hep-ph/0601225] [INSPIRE].
I.P. Ivanov, Two-Higgs-doublet model from the group-theoretic perspective, Phys. Lett. B 632 (2006) 360 [hep-ph/0507132] [INSPIRE].
C.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].
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].
I.P. 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].
P.M. 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].
P.M. Ferreira and J.P. Silva, Abelian symmetries in the two-Higgs-doublet model with fermions, Phys. Rev. D 83 (2011) 065026 [arXiv:1012.2874] [INSPIRE].
N.G. Deshpande and E. Ma, Pattern of symmetry breaking with two Higgs doublets, Phys. Rev. D 18 (1978) 2574 [INSPIRE].
B. Grzadkowski, M. Maniatis and J. Wudka, The bilinear formalism and the custodial symmetry in the two-Higgs-doublet model, JHEP 11 (2011) 030 [arXiv:1011.5228] [INSPIRE].
C.C. Nishi, Custodial SO(4) symmetry and CP-violation in N-Higgs-doublet potentials, Phys. Rev. D 83 (2011) 095005 [arXiv:1103.0252] [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].
P.S.B. Dev and A. Pilaftsis, Maximally symmetric two Higgs doublet model with natural standard model alignment, JHEP 12 (2014) 024 [arXiv:1408.3405] [INSPIRE].
I.P. 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].
I.P. Ivanov and C.C. Nishi, Symmetry breaking patterns in 3HDM, JHEP 01 (2015) 021 [arXiv:1410.6139] [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].
V.A. Solano et al., IntegerSmithNormalForm, Mathematica notebook, Wolfram Library Archive, http://library.wolfram.com/infocenter/MathSource/6621.
M. Leurer, Y. Nir and N. Seiberg, Mass matrix models, Nucl. Phys. B 398 (1993) 319 [hep-ph/9212278] [INSPIRE].
R. González Felipe et al., Constraining multi-Higgs flavour models, Eur. Phys. J. C 74 (2014) 2953 [arXiv:1401.5807] [INSPIRE].
G.C. Branco et al., Theory and phenomenology of two-Higgs-doublet models, Phys. Rept. 516 (2012) 1 [arXiv:1106.0034] [INSPIRE].
W. Grimus, A.S. Joshipura, L. Lavoura and M. Tanimoto, Symmetry realization of texture zeros, Eur. Phys. J. C 36 (2004) 227 [hep-ph/0405016] [INSPIRE].
H. Fritzsch and Z.-z. Xing, The light quark sector, CP-violation and the unitarity triangle, Nucl. Phys. B 556 (1999) 49 [hep-ph/9904286] [INSPIRE].
G.C. Branco, D. Emmanuel-Costa and R. Gonzalez Felipe, Texture zeros and weak basis transformations, Phys. Lett. B 477 (2000) 147 [hep-ph/9911418] [INSPIRE].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1411.4909
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Nishi, C.C. Compatible abelian symmetries in N-Higgs-doublet models. J. High Energ. Phys. 2015, 34 (2015). https://doi.org/10.1007/JHEP03(2015)034
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2015)034