Natural vacuum alignment from group theory: The minimal case

Journal of High Energy Physics

Volumn 2012, Issue 1, 2012, Pages

  Holthausen, Martin ^a   Schmidt, Michael A ^b,c  

^a MAX PLANCK INSTITUT FÜR KERNPHYSIK   (Germany)

^b DURHAM UNIVERSITY   (United Kingdom)

^c UNIVERSITY OF MELBOURNE   (Australia)

Author keywords

Beyond standard model; Discrete and finite symmetries; Neutrino physics

Indexed keywords

EID: 84857285940     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1007/JHEP01(2012)126     Document Type: Article

References (83)

1. T. Schwetz, M. Tortola and J. Valle, Where we are on 13: addendum to 'Global neutrino data and recent reactor uxes: status of three-avour oscillation parameters', New J. Phys. 13 (2011) 109401 [arXiv:1108.1376] [INSPIRE].
2. T. Schwetz, M. Tortola and J. Valle, Global neutrino data and recent reactor uxes: status of three-avour oscillation parameters, New J. Phys. 13 (2011) 063004 [arXiv:1103.0734] [INSPIRE].
3. G. Fogli, E. Lisi, A. Marrone, A. Palazzo and A. Rotunno, Evidence of 13 > 0 from global neutrino data analysis, Phys. Rev. D 84 (2011) 053007 [arXiv:1106.6028] [INSPIRE].
4. M. Gonzalez-Garcia, M. Maltoni and J. Salvado, Updated global t to three neutrino mixing: status of the hints of 13 > 0, JHEP 04 (2010) 056 [arXiv:1001.4524] [INSPIRE].
5. T2K collaboration, K. Abe et al., Indication of electron neutrino appearance from an accelerator-produced o-axis muon neutrino beam, Phys. Rev. Lett. 107 (2011) 041801 [arXiv:1106.2822] [INSPIRE].
6. CHOOZ collaboration, M. Apollonio et al., Search for neutrino oscillations on a long baseline at the CHOOZ nuclear power station, Eur. Phys. J. C 27 (2003) 331 [hep-ex/0301017] [INSPIRE].
7. P. Harrison, D. Perkins and W. Scott, A redetermination of the neutrino mass squared difference in tri-maximal mixing with terrestrial matter effects, Phys. Lett. B 458 (1999) 79 [hep-ph/9904297] [INSPIRE].
8. P. Harrison, D. Perkins and W. Scott, Tri-bimaximal mixing and the neutrino oscillation data, Phys. Lett. B 530 (2002) 167 [hep-ph/0202074] [INSPIRE].
9. P. Harrison and W. Scott, Symmetries and generalizations of tri-bimaximal neutrino mixing, Phys. Lett. B 535 (2002) 163 [hep-ph/0203209] [INSPIRE].
10. MINOS collaboration, P. Adamson et al., Improved search for muon-neutrino to electron-neutrino oscillations in MINOS, Phys. Rev. Lett. 107 (2011) 181802 [arXiv:1108.0015] [INSPIRE].
11. C.D. Froggatt H.B. Nielsen, Hierarchy of quark masses, Cabibbo angles and CP violation, Nucl. Phys. B 147 (1979) 277 [INSPIRE].
12. K. Babu and X.-G. He, Model of geometric neutrino mixing, hep-ph/0507217 [INSPIRE].
13. E. Ma, A4 symmetry and neutrinos with very different masses, Phys. Rev. D 70 (2004) 031901 [hep-ph/0404199] [INSPIRE].
14. K. Babu, E. Ma and J. Valle, Underlying A4 symmetry for the neutrino mass matrix and the quark mixing matrix, Phys. Lett. B 552 (2003) 207 [hep-ph/0206292] [INSPIRE].
15. E. Ma and G. Rajasekaran, Softly broken A4 symmetry for nearly degenerate neutrino masses, Phys. Rev. D 64 (2001) 113012 [hep-ph/0106291] [INSPIRE].
16. X.-G. He, Y.-Y. Keum and R.R. Volkas, A4 avor symmetry breaking scheme for understanding quark and neutrino mixing angles, JHEP 04 (2006) 039 [hep-ph/0601001] [INSPIRE].
17. G. Altarelli and F. Feruglio, Tri-bimaximal neutrino mixing, A4 and the modular symmetry, Nucl. Phys. B 741 (2006) 215 [hep-ph/0512103] [INSPIRE].
18. G. Altarelli and F. Feruglio, Tri-bimaximal neutrino mixing from discrete symmetry in extra dimensions, Nucl. Phys. B 720 (2005) 64 [hep-ph/0504165] [INSPIRE].
19. 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].
20. S. Pakvasa and H. Sugawara, Mass of the t quark in SU(2) U(1), Phys. Lett. B 82 (1979) 105 [INSPIRE].
21. Y. Yamanaka and H. Sugawara, Permutation symmetries and the fermion mass matrix, Phys. Rev. D 25 (1982) 1895 [Erratum ibid. D29 (1984) 2135+ [INSPIRE].
22. T. Brown et al., CP nonconservation and rare processes in S4 model of permutation symmetry, Phys. Lett. B 141 (1984) 95 [INSPIRE].
23. T. Brown et al., Neutrino masses, mixing and oscillations in S4 model of permutation symmetry, Phys. Rev. D 30 (1984) 255 [INSPIRE
24. D.-G. Lee and R. Mohapatra, An SO(10) S4 scenario for naturally degenerate neutrinos, Phys. Lett. B 329 (1994) 463 [hep-ph/9403201] [INSPIRE].
25. E. Ma, Neutrino mass matrix from S4 symmetry, Phys. Lett. B 632 (2006) 352 [hep-ph/0508231] [INSPIRE].
26. 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] [INSPIRE].
27. Y. Cai and H.-B. Yu, A SO(10) GUT model with S4 avor symmetry, Phys. Rev. D 74 (2006) 115005 [hep-ph/0608022] [INSPIRE].
28. F. Caravaglios and S. Morisi, Gauge boson families in grand unified theories of fermion masses: E4 6 S4, Int. J. Mod. Phys. A 22 (2007) 2469 [hep-ph/0611078] [INSPIRE].
29. H. Zhang, Flavor S4 Z(2) symmetry and neutrino mixing, Phys. Lett. B 655 (2007) 132 [hep-ph/0612214] [INSPIRE].
30. Y. Koide, S4 avor symmetry embedded into SU(3) and lepton masses and mixing, JHEP 08 (2007) 086 [arXiv:0705.2275] [INSPIRE].
31. M. Parida, Intermediate left-right gauge symmetry, unification of couplings and fermion masses in SUSY SO(10) S4, Phys. Rev. D 78 (2008) 053004 [arXiv:0804.4571] [INSPIRE].
32. F. Bazzocchi and S. Morisi, S4 as a natural avor symmetry for lepton mixing, Phys. Rev. D 80 (2009) 096005 [arXiv:0811.0345] [INSPIRE].
33. H. Ishimori, Y. Shimizu and M. Tanimoto, S4 avor symmetry of quarks and leptons in SU(5) GUT, Prog. Theor. Phys. 121 (2009) 769 [arXiv:0812.5031] [INSPIRE].
34. F. Bazzocchi, L. Merlo and S. Morisi, Phenomenological consequences of see-saw in S4 based models, Phys. Rev. D 80 (2009) 053003 [arXiv:0902.2849] [INSPIRE].
35. G. Altarelli, F. Feruglio and L. Merlo, Revisiting bimaximal neutrino mixing in a model with S4 discrete symmetry, JHEP 05 (2009) 020 [arXiv:0903.1940] [INSPIRE].
36. H. Ishimori, Y. Shimizu and M. Tanimoto, S4 avor model of quarks and leptons, Prog. Theor. Phys. Suppl. 180 (2010) 61 [arXiv:0904.2450] [INSPIRE].
37. W. Grimus, L. Lavoura and P. Ludl, Is S4 the horizontal symmetry of tri-bimaximal lepton mixing?, J. Phys. G 36 (2009) 115007 [arXiv:0906.2689] [INSPIRE].
38. G.-J. Ding, Fermion masses and avor mixings in a model with S4 avor symmetry, Nucl. Phys. B 827 (2010) 82 [arXiv:0909.2210] [INSPIRE].
39. D. Meloni, A see-saw S4 model for fermion masses and mixings, J. Phys. G 37 (2010) 055201 [arXiv:0911.3591] [INSPIRE].
40. S. Morisi and E. Peinado, An S4 model for quarks and leptons with maximal atmospheric angle, Phys. Rev. D 81 (2010) 085015 [arXiv:1001.2265] [INSPIRE].
41. B. Dutta, Y. Mimura and R. Mohapatra, An SO(10) grand uniffed theory of avor, JHEP 05 (2010) 034 [arXiv:0911.2242] [INSPIRE].
42. C. Lam, The unique horizontal symmetry of leptons, Phys. Rev. D 78 (2008) 073015 [arXiv:0809.1185] [INSPIRE].
43. R. Mohapatra, M. Parida and G. Rajasekaran, High scale mixing unification and large neutrino mixing angles, Phys. Rev. D 69 (2004) 053007 [hep-ph/0301234] [INSPIRE].
44. G.-J. Ding, Fermion mass hierarchies and avor mixing from T-prime symmetry, Phys. Rev. D 78 (2008) 036011 [arXiv:0803.2278] [INSPIRE].
45. P.H. Frampton and S. Matsuzaki, T-prime predictions of PMNS and CKM angles, Phys. Lett. B 679 (2009) 347 [arXiv:0902.1140] [INSPIRE].
46. P.H. Frampton and T.W. Kephart, Flavor symmetry for quarks and leptons, JHEP 09 (2007) 110 [arXiv:0706.1186] [INSPIRE].
47. A. Aranda, Neutrino mixing from the double tetrahedral group T-prime, Phys. Rev. D 76 (2007) 111301 [arXiv:0707.3661] [INSPIRE].
48. P.D. Carr and P.H. Frampton, Group theoretic bases for tribimaximal mixing, hep-ph/0701034 [INSPIRE].
49. F. Feruglio, C. Hagedorn, Y. Lin and L. Merlo, Tri-bimaximal neutrino mixing and quark masses from a discrete avour symmetry, Nucl. Phys. B 775 (2007) 120 [Erratum ibid. 836 (2010) 127-128] [hep-ph/0702194] [INSPIRE].
50. M.-C. Chen and K. Mahanthappa, CKM and tri-bimaximal MNS matrices in a SU(5) (d)T model, Phys. Lett. B 652 (2007) 34 [arXiv:0705.0714] [INSPIRE].
51. F. Bazzocchi and I. de Medeiros Varzielas, Tri-bi-maximal mixing in viable family symmetry uniffed model with extended seesaw, Phys. Rev. D 79 (2009) 093001 [arXiv:0902.3250] [INSPIRE].
52. C. Luhn, S. Nasri and P. Ramond, The avor group (3n2), J. Math. Phys. 48 (2007) 073501 [hep-th/0701188] [INSPIRE].
53. W. Grimus and L. Lavoura, A model for trimaximal lepton mixing, JHEP 09 (2008) 106 [arXiv:0809.0226] [INSPIRE].
54. I. de Medeiros Varzielas, S. King and G. Ross, Neutrino tri-bi-maximal mixing from a non-abelian discrete family symmetry, Phys. Lett. B 648 (2007) 201 [hep-ph/0607045] [INSPIRE].
55. Y. Shimizu, M. Tanimoto and A. Watanabe, Breaking tri-bimaximal mixing and large 13, Prog. Theor. Phys. 126 (2011) 81 [arXiv:1105.2929] [INSPIRE].
56. R.d.A. Toorop, F. Feruglio and C. Hagedorn, Discrete avour symmetries in light of T2K, Phys. Lett. B 703 (2011) 447 [arXiv:1107.3486] [INSPIRE].
57. T. Kobayashi, Y. Omura and K. Yoshioka, Flavor symmetry breaking and vacuum alignment on orbifolds, Phys. Rev. D 78 (2008) 115006 [arXiv:0809.3064] [INSPIRE].
58. K. Babu and S. Gabriel, Semidirect product groups, vacuum alignment and tribimaximal neutrino mixing, Phys. Rev. D 82 (2010) 073014 [arXiv:1006.0203] [INSPIRE].
59. GAP group, GAP - Groups, Algorithms, and Programming. Version 4.4.12, http://www.gap-system.org.
60. H.U. Besche, B. Eick and E.O'Brien, SmallGroups - Library of all 'small' groups. GAP package, version included in GAP 4.4.12 http://www.gap-system.org/ Packages/sgl.html.
61. K.M. Parattu and A. Wingerter, Tribimaximal mixing from small groups, Phys. Rev. D 84 (2011) 013011 [arXiv:1012.2842] [INSPIRE].
62. W. Grimus and P.O. Ludl, Finite avour groups of fermions, arXiv:1110.6376 [INSPIRE].
63. S.F. King and C. Luhn, On the origin of neutrino avour symmetry, JHEP 10 (2009) 093 [arXiv:0908.1897] [INSPIRE].
64. B. Brahmachari, S. Choubey and M. Mitra, The A4 avor symmetry and neutrino phenomenology, Phys. Rev. D 77 (2008) 073008 [Erratum ibid. D 77 (2008) 119901] [arXiv:0801.3554] [INSPIRE].
65. J. Barry and W. Rodejohann, Deviations from tribimaximal mixing due to the vacuum expectation value misalignment in A4 models, Phys. Rev. D 81 (2010) 093002 [Erratum ibid. D 81 (2010) 119901] [arXiv:1003.2385] [INSPIRE].
66. G. Altarelli, F. Feruglio and Y. Lin, Tri-bimaximal neutrino mixing from orbifolding, Nucl. Phys. B 775 (2007) 31 [hep-ph/0610165] [INSPIRE].
67. M. Honda and M. Tanimoto, Deviation from tri-bimaximal neutrino mixing in A4 avor symmetry, Prog. Theor. Phys. 119 (2008) 583 [arXiv:0801.0181] [INSPIRE].
68. S. Antusch, J. Kersten, M. Lindner, M. Ratz and M.A. Schmidt, Running neutrino mass parameters in see-saw scenarios, JHEP 03 (2005) 024 [hep-ph/0501272] [INSPIRE].
69. M. Lattanzi and J. Valle, Decaying warm dark matter and neutrino masses, Phys. Rev. Lett. 99 (2007) 121301 [arXiv:0705.2406] [INSPIRE].
70. P. Minkowski, et at a rate of one out of 1-billion muon decays?, Phys. Lett. B 67 (1977) 421 [INSPIRE].
71. T. Yanagida, Horizontal symmetry and masses of neutrinos, in the proceedings of the Workshop on the unified theory and the baryon number in the universe, O. Sawada ed., KEK, Tsukuba Japan (1979).
72. S.L. Glashow, The future of elementary particle physics, in the proceedings of the 1979 Cargffese summer institute on quarks and leptons, M. Levy et al. eds., Plenum Press, New York U.S.A. (1980).
73. M. Gell-Mann, P. Ramond and R. Slansky, Complex spinors and uniffed theories, in Supergravity, P. van Nieuwenhuizen and D.Z. Freedman eds., North Holland, Amsterdam The Netherlands (1979).
74. R.N. Mohapatra and G. Senjanovic, Neutrino mass and spontaneous parity violation, Phys. Rev. Lett. 44 (1980) 912 [INSPIRE].
75. J. Schechter and J.W.F. Valle, Neutrino masses in SU(2) U(1) theories, Phys. Rev. D 22 (1980) 2227 [INSPIRE].
76. J. Schechter and J.W.F. Valle, Neutrino decay and spontaneous violation of lepton number, Phys. Rev. D 25 (1982) 774 [INSPIRE].
77. M. Malinsky, J. Romao and J. Valle, Novel supersymmetric SO(10) seesaw mechanism, Phys. Rev. Lett. 95 (2005) 161801 [hep-ph/0506296] [INSPIRE].
78. F. Feruglio, C. Hagedorn and L. Merlo, Vacuum alignment in SUSY A4 models, JHEP 03 (2010) 084 [arXiv:0910.4058] [INSPIRE].
79. G. Giudice and R. Rattazzi, Theories with gauge mediated supersymmetry breaking, Phys. Rept. 322 (1999) 419 [hep-ph/9801271] [INSPIRE].
80. S. Antusch, S.F. King, M. Malinsky and G.G. Ross, Solving the SUSY avour and CP problems with non-abelian family symmetry and supergravity, Phys. Lett. B 670 (2009) 383 [arXiv:0807.5047] [INSPIRE].
81. V. Dabbaghian, REPSN - For constructing representations of finite groups, GAP package, Version 3.0.2, http://www.gap-system.org/Packages/repsn.html.
82. A. Merle and R. Zwicky, Explicit and spontaneous breaking of SU(3) into its finite subgroups, arXiv:1110.4891 [INSPIRE].
83. P.M. van Den Broek and J.F. Cornwell, Clebsch-Gordan coeffcients of symmetry groups, Phys. Status Solidi B 90 (1978) 211.