Explicit and spontaneous breaking of SU(3) into its finite subgroups

Journal of High Energy Physics

Volumn 2012, Issue 2, 2012, Pages

  Merle, Alexander ^a   Zwicky, Roman ^b  

^a ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

^b UNIVERSITY OF SOUTHAMPTON   (United Kingdom)

Author keywords

Beyond standard model; Discrete and finite symmetries; Spontaneous symmetry breaking

Indexed keywords

EID: 84857808986     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1007/JHEP02(2012)128     Document Type: Article

References (76)

1. P. Harrison, D. Perkins and W. Scott, Tri-bimaximal mixing and the neutrino oscillation data, Phys. Lett. B 530 (2002) 167 [hep-ph/0202074].
2. F. Caravaglios and S. Morisi, Neutrino masses and mixings with an S3 family permutation symmetry, hep-ph/0503234.
3. G. Altarelli and F. Feruglio, Tri-bimaximal neutrino mixing from discrete symmetry in extra dimensions, Nucl. Phys. B 720 (2005) 64 [hep-ph/0504165].
4. W. Grimus and L. Lavoura, A model realizing the Harrison-Perkins-Scott lepton mixing matrix, JHEP 01 (2006) 018 [hep-ph/0509239].
5. 4 and the modular symmetry, Nucl. Phys. B 741 (2006) 215 [hep-ph/0512103].
6. H.K. Dreiner, C. Luhn and M. Thormeier, What is the discrete gauge symmetry of the MSSM?, Phys. Rev. D 73 (2006) 075007 [hep-ph/0512163].
7. I. de Medeiros Varzielas, S. King and G. Ross, Tri-bimaximal neutrino mixing from discrete subgroups of SU(3) and SO(3) family symmetry, Phys. Lett. B 644 (2007) 153 [hep-ph/0512313].
8. C. Hagedorn, M. Lindner and R. Mohapatra, S4 avor symmetry and fermion masses: towards a grand unified theory of avor, JHEP 06 (2006) 042 [hep-ph/0602244].
9. S.F. King and M. Malinsky, A4 family symmetry and quark-lepton unification, Phys. Lett. B 645 (2007) 351 [hep-ph/0610250].
10. 4, Phys. Rev. D 75 (2007) 075015 [hep-ph/0702034].
11. 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].
12. 4 model for fermion masses and mixings, JHEP 03 (2008) 063 [arXiv:0707.3032].
13. 4, JHEP 03 (2008) 052 [arXiv:0802.0090].
14. F. Feruglio, C. Hagedorn, Y. Lin and L. Merlo, Lepton avour violation in models with A4 avour symmetry, Nucl. Phys. B 809 (2009) 218 [arXiv:0807.3160].
15. 4 symmetry, Phys. Rev. D 78 (2008) 116018 [arXiv:0809.3573].
16. 4 as a natural avor symmetry for lepton mixing, Phys. Rev. D 80 (2009) 096005 [arXiv:0811.0345].
17. F. Bazzocchi, L. Merlo and S. Morisi, Fermion masses and mixings in a S(4)-based model, Nucl. Phys. B 816 (2009) 204 [arXiv:0901.2086].
18. 4 based models, Phys. Rev. D 80 (2009) 053003 [arXiv:0902.2849].
19. M.-C. Chen and S.F. King, A4 see-saw models and form dominance, JHEP 06 (2009) 072 [arXiv:0903.0125].
20. 4 discrete symmetry, JHEP 05 (2009) 020 [arXiv:0903.1940].
21. 4 Model for Tri-Bimaximal Neutrino Mixing, J. Phys. G 36 (2009) 085005 [arXiv:0905.0620].
22. F. Feruglio, C. Hagedorn and L. Merlo, Vacuum alignment in SUSY A4 models, JHEP 03 (2010) 084 [arXiv:0910.4058].
23. 2(7) × SO(10), Nucl. Phys. B 832 (2010) 414 [arXiv:0912.1344].
24. 4 × SU(5) to NLO, JHEP 06 (2010) 048 [arXiv:1003.4249].
25. C. Hagedorn and M. Serone, Leptons in Holographic Composite Higgs Models with Non-Abelian Discrete Symmetries, JHEP 10 (2011) 083 [arXiv:1106.4021].
26. R.d.A. Toorop, F. Feruglio and C. Hagedorn, Discrete Flavour Symmetries in Light of T2K, Phys. Lett. B 703 (2011) 447 [arXiv:1107.3486].
27. 4 models, JHEP 09 (2011) 042 [arXiv:1107.5332].
28. W. Buchmüller and J. Schmidt, Higgs versus Matter in the Heterotic Landscape, Nucl. Phys. B 807 (2009) 265 [arXiv:0807.1046].
29. T. Kobayashi, H.P. Nilles, F. Ploger, S. Raby and M. Ratz, Stringy origin of non-Abelian discrete avor symmetries, Nucl. Phys. B 768 (2007) 135 [hep-ph/0611020].
30. A. Adulpravitchai, A. Blum and M. Lindner, Non-Abelian Discrete Groups from the Breaking of Continuous Flavor Symmetries, JHEP 09 (2009) 018 [arXiv:0907.2332].
31. W. Burnside, Theory of groups of finite order, second edition, Cambridge University Press, Cambridge U.K. (1897).
32. E. Noether, Der Endlichkeitssatz der Invarianten endlicher Gruppen (in German), Math. Ann. 77 (1916) 89.
33. B. Sturmfels, Algorithms in Invariant Theory, Texts and Monographs in Symbolic Computation, Springer, Heidelberg Germany (1993).
34. B. Meyer, On the symmetries of spherical harmonics, Canad. J. Math. 6 (1954) 135.
35. M. Koca, M. Al-Barwani and R. Koc, Breaking SO(3) into its closed subgroups by Higgs mechanism, J. Phys. A 30 (1997) 2109.
36. J. Patera and R.T. Sharp, Generating Functions For Characters Of Group Representations And Their Applications, Lect. Notes Phys. 94 (1979) 175.
37. T. Molien, Über die Invarianten der linearen Substitutionsgruppen (in German), Sitzungber. Konig. Preuss. Akad. Wiss. (J. Berl. Ber.) 52 (1897) 1152.
38. J.D. Dixon and B. Mortimer, Permutation Groups, Graduate Texts in Mathematics, Springer, Heidelberg Germany (1996).
39. L. O'Raifeartaigh, Group Structure Of Gauge Theories, Cambridge Monographs On Mathematical Physics, Cambridge University Press, Cambridge U.K. (1986).
40. L. Michel, Symmetry defects and broken symmetry. Configurations | hidden symmetry, Rev. Mod. Phys. 52 (1980) 617.
41. M.J. Linehan and G.E. Stedman, Little groups of irreps of O(3), SO(3), and the infinite axial subgroups, J. Phys. A 34 (2001) 6663 [math-ph/0012008].
42. 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].
43. G.A. Miller, H.F. Blichfeldt and L.E. Dickson, Theory and Applications of Finite Groups, John Wiley & Sons, New York U.S.A. (1916) [Dover, New York U.S.A. (1961)].
44. L. Michel and B.I. Zhilinskii, Symmetry, Invariants, and Topology. I. Basic Tools, Phys. Rept. 341 (2001) 11.
45. K.M. Parattu and A. Wingerter, Tribimaximal Mixing From Small Groups, Phys. Rev. D 84 (2011) 013011 [arXiv:1012.2842].
46. 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].
47. W. Fairbairn and T. Fulton, Some comments on finite subgroups of SU(3), J. Math. Phys. 23 (1982) 1747.
48. A. Bovier, M. Luling and D. Wyler, Representations and Clebsch-Gordan coefficients of Z metacyclic groups, J. Math. Phys. 22 (1981) 1536.
49. B. Durhuus, T. Jonsson and J.F. Wheater, Random walks on combs, J. Phys. A 39 (2006) 1009 [hep-th/0509191].
50. The GAP Group, GAP | Groups, Algorithms, and Programming, Version 4.4.12, (2008) http://www.gap-system.org.
51. H.U. Besche, B. Eick and E.A. O'Brien, SmallGroups | a GAP package (2002), http://www.gap-system.org/Packages/sgl.html, http://www.icm.tu-bs.de/ agalgebra/software/small/.
52. J.E. Humphreys, Reection groups and Coxeter groups, Cambridge University Press, Cambridge U.K. (1990).
53. P.O. Ludl, Comments on the classification of the finite subgroups of SU(3), J. Phys. A 44 (2011) 255204 [arXiv:1101.2308].
54. W. Grimus and P.O. Ludl, Finite avour groups of fermions, arXiv:1110.6376.
55. P.O. Ludl, Systematic analysis of finite family symmetry groups and their application to the lepton sector, arXiv:0907.5587.
56. R. Zwicky and T. Fischbacher, On discrete minimal avour violation, Phys. Rev. D 80 (2009) 076009 [arXiv:0908.4182].
57. C. Luhn, Spontaneous breaking of SU(3) to finite family symmetries: a pedestrian's approach, JHEP 03 (2011) 108 [arXiv:1101.2417].
58. P. Di Francesco, P. Mathieu and D. Senechal, Conformal field theory, Springer, New York U.S.A. (1997), pg. 890.
59. P. Ramond, Group Theory in Physics. A physicists survey, Cambridge University Press, Cambridge U.K. (2010).
60. J.F. Cornwell, Group Theory in Physics, Vol. 1, Academic Press, New York U.S.A. (1997).
61. W. Specht, Zur Theorie der Gruppen linearer Substitutionen. II. (in German), Jber. Deutsch. Math. Verein. 49 (1940) 207.
62. A. Hanany and Y.-H. He, A Monograph on the classification of the discrete subgroups of SU(4), JHEP 02 (2001) 027 [hep-th/9905212].
63. 5 Family Symmetry and the Golden Ratio Prediction for Solar Neutrino Mixing, Phys. Rev. D 79 (2009) 085005 [arXiv:0812.1057].
64. G. Etesi, Spontaneous symmetry breaking in SO(3) gauge theory to discrete subgroups, J. Math. Phys. 37 (1996) 1596 [hep-th/9706029].
65. 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].
66. M. Holthausen and M.A. Schmidt, Natural Vacuum Alignment from Group Theory: The Minimal Case, JHEP 01 (2012) 126 [arXiv:1111.1730].
67. 4, JHEP 02 (2010) 071 [arXiv:0910.4392].
68. G. Altarelli and F. Feruglio, Discrete Flavor Symmetries and Models of Neutrino Mixing, Rev. Mod. Phys. 82 (2010) 2701 [arXiv:1002.0211].
69. J. Patera, R.T. Sharp and P. Winternitz, Polynomial irreducible tensors for point groups, J. Math. Phys. 19 (1978) 2362.
70. R. King, J. Patera and R.T. Sharp, On finite and continuous little groups of representations of semi-simple Lie groups, J. Phys. A 15 (1982) 1143.
71. P. Desmier, R. Sharp and J. Patera, Analytic SU(3) states in a finite subgroup basis, J. Math. Phys. 23 (1982) 1393.
72. J.D. Louck, Unitary symmetry and combinatorics, World Scientific, New York U.S.A. (2008).
73. M. Ikeda, On Complex Spherical Harmonics, Prog. Theor. Phys. 32 (1964) 178.
74. T. Kayama, On the normalization of solid harmonics for U(3), Prog. Theor. Phys. 39 (1968) 850.
75. H. Georgi, Frontiers in Physics. Vol. 54: Lie Algebras in Particle Physics. From Isospin to Unified Theories, Westview Press, Boulder U.S.A. (1982).
76. R. Slansky, Group Theory for Unified Model Building, Phys. Rept. 79 (1981) 1.