Abstract
Many models of beyond Standard Model physics connect flavor symmetry with a discrete group. Having this symmetry arise spontaneously from a gauge theory maintains compatibility with quantum gravity and can be used to systematically prevent anomalies. We minimize a number of Higgs potentials that break gauge groups to discrete symmetries of interest, and examine their scalar mass spectra.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S. Pakvasa and H. Sugawara, Discrete symmetry and Cabibbo angle, Phys. Lett. B 73 (1978) 61.
D. Wyler, Discrete symmetries in the six quark SU(2) × U(1) model, Phys. Rev. D 19 (1979) 3369 [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].
K.S. Babu, E. Ma and J.W.F. Valle, Underlying A 4 symmetry for the neutrino mass matrix and the quark mixing matrix, Phys. Lett. B 552 (2003) 207 [hep-ph/0206292] [INSPIRE].
P.H. Frampton and T.W. Kephart, Simple nonAbelian finite flavor groups and fermion masses, Int. J. Mod. Phys. A 10 (1995) 4689 [hep-ph/9409330] [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].
G. Altarelli and F. Feruglio, Discrete flavor symmetries and models of neutrino mixing, Rev. Mod. Phys. 82 (2010) 2701 [arXiv:1002.0211] [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.F. King, A. Merle, S. Morisi, Y. Shimizu and M. Tanimoto, Neutrino mass and mixing: from theory to experiment, New J. Phys. 16 (2014) 045018 [arXiv:1402.4271] [INSPIRE].
L.M. Krauss and F. Wilczek, Discrete gauge symmetry in continuum theories, Phys. Rev. Lett. 62 (1989) 1221 [INSPIRE].
R. Holman et al., Solutions to the strong CP problem in a world with gravity, Phys. Lett. B 282 (1992) 132 [hep-ph/9203206] [INSPIRE];
M. Kamionkowski and J. March-Russell, Planck scale physics and the Peccei-Quinn mechanism, Phys. Lett. B 282 (1992) 137 [hep-th/9202003] [INSPIRE].
S.M. Barr and D. Seckel, Planck scale corrections to axion models, Phys. Rev. D 46 (1992) 539 [INSPIRE].
C. Luhn and P. Ramond, Anomaly conditions for non-abelian finite family symmetries, JHEP 07 (2008) 085 [arXiv:0805.1736] [INSPIRE].
M.B. Hindmarsh and T.W.B. Kibble, Cosmic strings, Rept. Prog. Phys. 58 (1995) 477 [hep-ph/9411342] [INSPIRE].
O. Reynolds, On the dynamical theory of incompressible viscous fluids and the determination of the criterion, Phil. Trans. Roy. Soc. A 186 (1895) 123.
B. Sturmfels, Algorithms in invariant theory, 2nd ed., Springer, Germmany (2008).
T. Molien, Uber die Invarianten der linearen Substitutionsgruppen, Sitz. König Preuss. Akad. Wiss. 52 (1897) 1152.
C. Luhn, Spontaneous breaking of SU(3) to finite family symmetries: a pedestrian’s approach, JHEP 03 (2011) 108 [arXiv:1101.2417] [INSPIRE].
A. Merle and R. Zwicky, Explicit and spontaneous breaking of SU(3) into its finite subgroups, JHEP 02 (2012) 128 [arXiv:1110.4891] [INSPIRE].
M. Fallbacher, Breaking classical Lie groups to finite subgroups — An automated approach, Nucl. Phys. B 898 (2015) 229 [arXiv:1506.03677] [INSPIRE].
GAP — Groups, Algorithms, Programming — A system for computational discrete algebra, version 4.8.5 (2016).
P.H. Frampton, T.W. Kephart and R.M. Rohm, A note on embedding nonabelian finite flavor groups in continuous groups, Phys. Lett. B 679 (2009) 478 [arXiv:0904.0420] [INSPIRE].
J. Berger and Y. Grossman, Model of leptons from SO(3) → A 4, JHEP 02 (2010) 071 [arXiv:0910.4392] [INSPIRE].
E. Ma, Neutrino mixing: A 4 variations, Phys. Lett. B 752 (2016) 198 [arXiv:1510.02501] [INSPIRE].
G. Altarelli, F. Feruglio and C. Hagedorn, A SUSY SU(5) grand unified model of tri-bimaximal mixing from A 4, JHEP 03 (2008) 052 [arXiv:0802.0090] [INSPIRE].
S.F. King and C. Luhn, A 4 models of tri-bimaximal-reactor mixing, JHEP 03 (2012) 036 [arXiv:1112.1959] [INSPIRE].
P.M. Ferreira, L. Lavoura and P.O. Ludl, A new A 4 model for lepton mixing, Phys. Lett. B 726 (2013) 767 [arXiv:1306.1500] [INSPIRE].
P. Cvitanovic, Group theory for Feynman diagrams in non-Abelian gauge theories, Phys. Rev. D 14 (1976) 1536 [INSPIRE].
C. Hagedorn, M. Lindner and R.N. Mohapatra, S 4 flavor symmetry and fermion masses: towards a grand unified theory of flavor, JHEP 06 (2006) 042 [hep-ph/0602244] [INSPIRE].
C. Hagedorn, S.F. King and C. Luhn, A SUSY GUT of Flavour with S 4 × SU(5) to NLO, JHEP 06 (2010) 048 [arXiv:1003.4249] [INSPIRE].
L.L. Everett and A.J. Stuart, Icosahedral (A 5 ) family symmetry and the golden ratio prediction for solar neutrino mixing, Phys. Rev. D 79 (2009) 085005 [arXiv:0812.1057] [INSPIRE].
F. Feruglio and A. Paris, The golden ratio prediction for the solar angle from a natural model with A 5 flavour symmetry, JHEP 03 (2011) 101 [arXiv:1101.0393] [INSPIRE].
G.-J. Ding, L.L. Everett and A.J. Stuart, Golden ratio neutrino mixing and A 5 flavor symmetry, Nucl. Phys. B 857 (2012) 219 [arXiv:1110.1688] [INSPIRE].
C.-S. Chen, T.W. Kephart and T.-C. Yuan, An A 5 model of four lepton generations, JHEP 04 (2011) 015 [arXiv:1011.3199] [INSPIRE].
P.H. Frampton and T.W. Kephart, Minimal family unification, Phys. Rev. D 51 (1995) R1 [hep-ph/9409324] [INSPIRE].
P.H. Frampton and A. Rasin, NonAbelian discrete symmetries, fermion mass textures and large neutrino mixing, Phys. Lett. B 478 (2000) 424 [hep-ph/9910522] [INSPIRE].
A. Aranda, C.D. Carone and R.F. Lebed, U(2) flavor physics without U(2) symmetry, Phys. Lett. B 474 (2000) 170 [hep-ph/9910392] [INSPIRE].
M.-C. Chen and K.T. Mahanthappa, CKM and tri-bimaximal MNS matrices in a SU(5) × (d) T model, Phys. Lett. B 652 (2007) 34 [arXiv:0705.0714] [INSPIRE].
P.H. Frampton and T.W. Kephart, Flavor symmetry for quarks and leptons, JHEP 09 (2007) 110 [arXiv:0706.1186] [INSPIRE].
P.H. Frampton, T.W. Kephart and S. Matsuzaki, Simplified renormalizable T-prime model for tribimaximal mixing and Cabibbo angle, Phys. Rev. D 78 (2008) 073004 [arXiv:0807.4713] [INSPIRE].
P.H. Frampton, C.M. Ho, T.W. Kephart and S. Matsuzaki, LHC Higgs production and decay in the T ′ model, Phys. Rev. D 82 (2010) 113007 [arXiv:1009.0307] [INSPIRE].
A. Natale, A radiative model of quark masses with binary tetrahedral symmetry, Nucl. Phys. B 914 (2017) 201 [arXiv:1608.06999] [INSPIRE].
C.D. Carone, S. Chaurasia and S. Vasquez, Flavor from the double tetrahedral group without supersymmetry, Phys. Rev. D 95 (2017) 015025 [arXiv:1611.00784] [INSPIRE].
L.L. Everett and A.J. Stuart, The double cover of the icosahedral symmetry group and quark mass textures, Phys. Lett. B 698 (2011) 131 [arXiv:1011.4928] [INSPIRE].
C.-S. Chen, T.W. Kephart and T.-C. Yuan, Binary icosahedral flavor symmetry for four generations of quarks and leptons, PTEP 2013 (2013) 103B01 [arXiv:1110.6233] [INSPIRE].
C. Luhn, S. Nasri and P. Ramond, Tri-bimaximal neutrino mixing and the family symmetry semidirect product of Z 7 and Z 3, Phys. Lett. B 652 (2007) 27 [arXiv:0706.2341] [INSPIRE].
J. Kile, M.J. Pérez, P. Ramond and J. Zhang, θ 13 and the flavor ring, Phys. Rev. D 90 (2014) 013004 [arXiv:1403.6136] [INSPIRE].
V.V. Vien, T 7 flavor symmetry scheme for understanding neutrino mass and mixing in 3-3-1 model with neutral leptons, Mod. Phys. Lett. A 29 (2014) 28 [arXiv:1508.02585] [INSPIRE].
V.V. Vien and H.N. Long, Lepton mass and mixing in a simple extension of the Standard Model based on T 7 flavor symmetry, arXiv:1609.03895 [INSPIRE].
V.V. Vien, A.E. Cárcamo Hernández and H.N. Long, The Δ(27) flavor 3-3-1 model with neutral leptons, Nucl. Phys. B 913 (2016) 792 [arXiv:1601.03300] [INSPIRE].
P.M. Ferreira, W. Grimus, L. Lavoura and P.O. Ludl, Maximal CP-violation in lepton mixing from a model with Δ(27) flavour Symmetry, JHEP 09 (2012) 128 [arXiv:1206.7072] [INSPIRE].
G. Chen, M.J. Pérez and P. Ramond, Neutrino masses, the μ-term and PSL2(7), Phys. Rev. D 92 (2015) 076006 [arXiv:1412.6107] [INSPIRE].
M. Koca, R. Koc and H. Tutunculer, Explicit breaking of SO(3) with Higgs fields in the representations l = 2 and l = 3, Int. J. Mod. Phys. A 18 (2003) 4817 [hep-ph/0410270] [INSPIRE].
C. Luhn, private communication.
C. Hagedorn, M.A. Schmidt and A. Yu. Smirnov, Lepton mixing and cancellation of the Dirac mass hierarchy in SO(10) GUTs with flavor symmetries T 7 and Σ(81), Phys. Rev. D 79 (2009) 036002 [arXiv:0811.2955] [INSPIRE].
S.F. King, C. Luhn and A.J. Stuart, A grand Δ(96) × SU(5) flavour model, Nucl. Phys. B 867 (2013) 203 [arXiv:1207.5741] [INSPIRE].
V.V. Vien and H.N. Long, Quark masses and mixings in the 3-3-1 model with neutral leptons based on D 4 flavor symmetry, J. Korean Phys. Soc. 66 (2015) 1809 [arXiv:1408.4333] [INSPIRE].
P.O. Ludl, On the finite subgroups of U(3) of order smaller than 512, J. Phys. A 43 (2010) 395204 [Erratum ibid. A 44 (2011) 139501] [arXiv:1006.1479] [INSPIRE].
W. Grimus and P.O. Ludl, Finite flavour groups of fermions, J. Phys. A 45 (2012) 233001 [arXiv:1110.6376] [INSPIRE].
P.O. Ludl, Comments on the classification of the finite subgroups of SU(3), J. Phys. A 44 (2011) 255204 [Erratum ibid. A 45 (2012) 069502] [arXiv:1101.2308] [INSPIRE].
W.-C. Huang, Y.-L.S. Tsai and T.-C. Yuan, G2HDM: gauged two Higgs doublet model, JHEP 04 (2016) 019 [arXiv:1512.00229] [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: 1702.08073
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
Rachlin, B.L., Kephart, T.W. Spontaneous breaking of gauge groups to discrete symmetries. J. High Energ. Phys. 2017, 110 (2017). https://doi.org/10.1007/JHEP08(2017)110
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2017)110