Advertisement

Strong coupling, discrete symmetry and flavour

  • Steven Abel
  • James Barnard
Article

Abstract

We show how two principles — strong coupling and discrete symmetry — can work together to generate the flavour structure of the Standard Model. We propose that in the UV the full theory has a discrete flavour symmetry, typically only associated with tribimaximal mixing in the neutrino sector. Hierarchies in the particle masses and mixing matrices then emerge from multiple strongly coupled sectors that break this symmetry. This allows for a realistic flavour structure, even in models built around an underlying grand unified theory. We use two different techniques to understand the strongly coupled physics: confinement in \( \mathcal{N} = 1 \) supersymmetry and the AdS/CFT correspondence. Both approaches yield equivalent results and can be represented in a clear, graphical way where the flavour symmetry is realised geometrically.

Keywords

Confinement Discrete and Finite Symmetries Supersymmetry and Duality Large Extra Dimensions 

References

  1. [1]
    I. Affleck, M. Dine and N. Seiberg, Supersymmetry Breaking by Instantons, Phys. Rev. Lett. 51 (1983) 1026 [SPIRES].MathSciNetADSGoogle Scholar
  2. [2]
    I. Affleck, M. Dine and N. Seiberg, Dynamical Supersymmetry Breaking in Supersymmetric QCD, Nucl. Phys. B 241 (1984) 493 [SPIRES].ADSGoogle Scholar
  3. [3]
    I. Affleck, M. Dine and N. Seiberg, Dynamical Supersymmetry Breaking in Four-Dimensions and Its Phenomenological Implications, Nucl. Phys. B 256 (1985) 557 [SPIRES].MathSciNetADSGoogle Scholar
  4. [4]
    N. Seiberg, Electric-magnetic duality in supersymmetric non-Abelian gauge theories, Nucl. Phys. B 435 (1995) 129 [hep-th/9411149] [SPIRES].MathSciNetADSGoogle Scholar
  5. [5]
    K.A. Intriligator and N. Seiberg, Lectures on supersymmetric gauge theories and electric-magnetic duality, Nucl. Phys. Proc. Suppl. 45BC (1996) 1 [hep-th/9509066] [SPIRES].MATHMathSciNetADSGoogle Scholar
  6. [6]
    M.J. Strassler, Generating a Fermion Mass Hierarchy in a Composite Supersymmetric Standard Model, Phys. Lett. B 376 (1996) 119 [hep-ph/9510342] [SPIRES].MathSciNetADSGoogle Scholar
  7. [7]
    A.E. Nelson and M.J. Strassler, A realistic supersymmetric model with composite quarks, Phys. Rev. D 56 (1997) 4226 [hep-ph/9607362] [SPIRES].ADSGoogle Scholar
  8. [8]
    M. Berkooz, P.L. Cho, P. Kraus and M.J. Strassler, Dual descriptions of SO(10) SUSY gauge theories with arbitrary numbers of spinors and vectors, Phys. Rev. D 56 (1997) 7166 [hep-th/9705003] [SPIRES].ADSGoogle Scholar
  9. [9]
    N. Arkani-Hamed, M.A. Luty and J. Terning, Composite quarks and leptons from dynamical supersymmetry breaking without messengers, Phys. Rev. D 58 (1998) 015004 [hep-ph/9712389] [SPIRES].ADSGoogle Scholar
  10. [10]
    M.A. Luty and J. Terning, Improved single sector supersymmetry breaking, Phys. Rev. D 62 (2000) 075006 [hep-ph/9812290] [SPIRES].ADSGoogle Scholar
  11. [11]
    A.E. Nelson and M.J. Strassler, Suppressing flavor anarchy, JHEP 09 (2000) 030 [hep-ph/0006251] [SPIRES].ADSGoogle Scholar
  12. [12]
    R.R. Volkas and G.C. Joshi, Supersymmetric composite models, Phys. Rept. 159 (1988) 303 [SPIRES].ADSGoogle Scholar
  13. [13]
    S. Franco and S. Kachru, Single-Sector Supersymmetry Breaking in Supersymmetric QCD, Phys. Rev. D 81 (2010) 095020 [arXiv:0907.2689] [SPIRES].ADSGoogle Scholar
  14. [14]
    D. Poland and D. Simmons-Duffin, Superconformal Flavor Simplified, JHEP 05 (2010) 079 [arXiv:0910.4585] [SPIRES].ADSGoogle Scholar
  15. [15]
    N. Craig, R. Essig, S. Franco, S. Kachru and G. Torroba, Dynamical Supersymmetry Breaking, with Flavor, Phys. Rev. D 81 (2010) 075015 [arXiv:0911.2467] [SPIRES].ADSGoogle Scholar
  16. [16]
    F. del Aguila, A. Carmona and J. Santiago, Neutrino Masses from an A 4 Symmetry in Holographic Composite Higgs Models, arXiv:1001.5151 [SPIRES].
  17. [17]
    A. Kadosh and E. Pallante, An A 4 flavor model for quarks and leptons in warped geometry, arXiv:1004.0321 [SPIRES].
  18. [18]
    N. Craig, Simple Models of Superconformal Flavor, arXiv:1004.4218 [SPIRES].
  19. [19]
    S. Schäfer-Nameki, C. Tamarit and G. Torroba, A Hybrid Higgs, arXiv:1005.0841 [SPIRES].
  20. [20]
    G. Altarelli and F. Feruglio, Discrete Flavor Symmetries and Models of Neutrino Mixing, arXiv:1002.0211 [SPIRES].
  21. [21]
    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] [SPIRES].ADSGoogle Scholar
  22. [22]
    G. Altarelli, F. Feruglio and Y. Lin, Tri-bimaximal neutrino mixing from orbifolding, Nucl. Phys. B 775 (2007) 31 [hep-ph/0610165] [SPIRES].ADSGoogle Scholar
  23. [23]
    C. Csáki, C. Delaunay, C. Grojean and Y. Grossman, A Model of Lepton Masses from a Warped Extra Dimension, JHEP 10 (2008) 055 [arXiv:0806.0356] [SPIRES].ADSGoogle Scholar
  24. [24]
    E. Ma and G. Rajasekaran, Softly broken A4 symmetry for nearly degenerate neutrino masses, Phys. Rev. D 64 (2001) 113012 [hep-ph/0106291] [SPIRES].ADSGoogle Scholar
  25. [25]
    E. Ma, Quark Mass Matrices in the A 4 Model, Mod. Phys. Lett. A 17 (2002) 627 [hep-ph/0203238] [SPIRES].ADSGoogle Scholar
  26. [26]
    M. Hirsch, J.C. Romao, S. Skadhauge, J.W.F. Valle and A. Villanova del Moral, Phenomenological tests of supersymmetric A 4 family symmetry model of neutrino mass, Phys. Rev. D 69 (2004) 093006 [hep-ph/0312265] [SPIRES].ADSGoogle Scholar
  27. [27]
    E. Ma, A 4 origin of the neutrino mass matrix, Phys. Rev. D 70 (2004) 031901 [hep-ph/0404199] [SPIRES].ADSGoogle Scholar
  28. [28]
    E. Ma, Non-Abelian discrete symmetries and neutrino masses: Two examples, New J. Phys. 6 (2004) 104 [hep-ph/0405152] [SPIRES].ADSGoogle Scholar
  29. [29]
    G. Altarelli and F. Feruglio, Tri-bimaximal neutrino mixing from discrete symmetry in extra dimensions, Nucl. Phys. B 720 (2005) 64 [hep-ph/0504165] [SPIRES].ADSGoogle Scholar
  30. [30]
    S.-L. Chen, M. Frigerio and E. Ma, Hybrid seesaw neutrino masses with A 4 family symmetry, Nucl. Phys. B 724 (2005) 423 [hep-ph/0504181] [SPIRES].ADSGoogle Scholar
  31. [31]
    E. Ma, Aspects of the tetrahedral neutrino mass matrix, Phys. Rev. D 72 (2005) 037301 [hep-ph/0505209] [SPIRES].ADSGoogle Scholar
  32. [32]
    M. Hirsch, A. Villanova del Moral, J.W.F. Valle and E. Ma, Predicting neutrinoless double beta decay, Phys. Rev. D 72 (2005) 091301 [hep-ph/0507148] [SPIRES].ADSGoogle Scholar
  33. [33]
    K.S. Babu and X.-G. He, Model of geometric neutrino mixing, hep-ph/0507217 [SPIRES].
  34. [34]
    E. Ma, Tetrahedral family symmetry and the neutrino mixing matrix, Mod. Phys. Lett. A 20 (2005) 2601 [hep-ph/0508099] [SPIRES].ADSGoogle Scholar
  35. [35]
    A. Zee, Obtaining the neutrino mixing matrix with the tetrahedral group, Phys. Lett. B 630 (2005) 58 [hep-ph/0508278] [SPIRES].MathSciNetADSGoogle Scholar
  36. [36]
    E. Ma, Tribimaximal neutrino mixing from a supersymmetric model with A 4 family symmetry, Phys. Rev. D 73 (2006) 057304 [hep-ph/0511133] [SPIRES].ADSGoogle Scholar
  37. [37]
    G. Altarelli and F. Feruglio, Tri-Bimaximal Neutrino Mixing, A 4 and the Modular Symmetry, Nucl. Phys. B 741 (2006) 215 [hep-ph/0512103] [SPIRES].MathSciNetADSGoogle Scholar
  38. [38]
    X.-G. He, Y.-Y. Keum and R.R. Volkas, A 4 flavour symmetry breaking scheme for understanding quark and neutrino mixing angles, JHEP 04 (2006) 039 [hep-ph/0601001] [SPIRES].ADSGoogle Scholar
  39. [39]
    B. Adhikary, B. Brahmachari, A. Ghosal, E. Ma and M.K. Parida, A 4 symmetry and prediction of U(e3) in a modified Altarelli-Feruglio model, Phys. Lett. B 638 (2006) 345 [hep-ph/0603059] [SPIRES].ADSGoogle Scholar
  40. [40]
    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] [SPIRES].ADSGoogle Scholar
  41. [41]
    L. Lavoura and H. Kuhbock, Predictions of an A 4 model with a five-parameter neutrino mass matrix, Mod. Phys. Lett. A 22 (2007) 181 [hep-ph/0610050] [SPIRES].ADSGoogle Scholar
  42. [42]
    E. Ma, Supersymmetric A 4 × Z 3 and A 4 Realizations of Neutrino Tribimaximal Mixing Without and With Corrections, Mod. Phys. Lett. A 22 (2007) 101 [hep-ph/0610342] [SPIRES].ADSGoogle Scholar
  43. [43]
    M. Hirsch, A.S. Joshipura, S. Kaneko and J.W.F. Valle, Predictive flavour symmetries of the neutrino mass matrix, Phys. Rev. Lett. 99 (2007) 151802 [hep-ph/0703046] [SPIRES].ADSGoogle Scholar
  44. [44]
    F. Yin, Neutrino mixing matrix in the 3-3-1 model with heavy leptons and A 4 symmetry, Phys. Rev. D 75 (2007) 073010 [arXiv:0704.3827] [SPIRES].ADSGoogle Scholar
  45. [45]
    F. Bazzocchi, S. Kaneko and S. Morisi, A SUSY A 4 model for fermion masses and mixings, JHEP 03 (2008) 063 [arXiv:0707.3032] [SPIRES].MathSciNetADSGoogle Scholar
  46. [46]
    F. Bazzocchi, S. Morisi and M. Picariello, Embedding A 4 into left-right flavor symmetry: Tribimaximal neutrino mixing and fermion hierarchy, Phys. Lett. B 659 (2008) 628 [arXiv:0710.2928] [SPIRES].ADSGoogle Scholar
  47. [47]
    M. Honda and M. Tanimoto, Deviation from tri-bimaximal neutrino mixing in A 4 flavor symmetry, Prog. Theor. Phys. 119 (2008) 583 [arXiv:0801.0181] [SPIRES].MATHADSGoogle Scholar
  48. [48]
    B. Brahmachari, S. Choubey and M. Mitra, The A4 flavor symmetry and neutrino phenomenology, Phys. Rev. D 77 (2008) 073008 [arXiv:0801.3554] [SPIRES].ADSGoogle Scholar
  49. [49]
    B. Adhikary and A. Ghosal, Nonzero U e3 , CP-violation and leptogenesis in a see-saw type softly broken A 4 symmetric model, Phys. Rev. D 78 (2008) 073007 [arXiv:0803.3582] [SPIRES].ADSGoogle Scholar
  50. [50]
    M. Hirsch, S. Morisi and J.W.F. Valle, Tri-bimaximal neutrino mixing and neutrinoless double beta decay, Phys. Rev. D 78 (2008) 093007 [arXiv:0804.1521] [SPIRES].ADSGoogle Scholar
  51. [51]
    Y. Lin, A predictive A 4 model, Charged Lepton Hierarchy and Tri- bimaximal Sum Rule, Nucl. Phys. B 813 (2009) 91 [arXiv:0804.2867] [SPIRES].ADSGoogle Scholar
  52. [52]
    P.H. Frampton and S. Matsuzaki, Renormalizable A 4 Model for Lepton Sector, arXiv:0806.4592 [SPIRES].
  53. [53]
    S. Morisi, Tri-Bimaximal lepton mixing with A4 semidirect product Z2 × Z2 × Z2, Phys. Rev. D 79 (2009) 033008 [arXiv:0901.1080] [SPIRES].ADSGoogle Scholar
  54. [54]
    Y. Lin, A dynamical approach to link low energy phases with leptogenesis, Phys. Rev. D 80 (2009) 076011 [arXiv:0903.0831] [SPIRES].ADSGoogle Scholar
  55. [55]
    G. Altarelli and D. Meloni, A Simplest A4 Model for Tri-Bimaximal Neutrino Mixing, J. Phys. G 36 (2009) 085005 [arXiv:0905.0620] [SPIRES].ADSGoogle Scholar
  56. [56]
    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] [SPIRES].MathSciNetADSGoogle Scholar
  57. [57]
    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] [SPIRES].ADSGoogle Scholar
  58. [58]
    A. Aranda, C.D. Carone and R.F. Lebed, Maximal neutrino mixing from a minimal flavor symmetry, Phys. Rev. D 62 (2000) 016009 [hep-ph/0002044] [SPIRES].ADSGoogle Scholar
  59. [59]
    F. Feruglio, C. Hagedorn, Y. Lin and L. Merlo, Tri-bimaximal Neutrino Mixing and Quark Masses from a Discrete Flavour Symmetry, Nucl. Phys. B 775 (2007) 120 [hep-ph/0702194] [SPIRES].ADSGoogle Scholar
  60. [60]
    P.H. Frampton and T.W. Kephart, Flavor Symmetry for Quarks and Leptons, JHEP 09 (2007) 110 [arXiv:0706.1186] [SPIRES].ADSGoogle Scholar
  61. [61]
    P.H. Frampton and T.W. Kephart, Flavor Symmetry for Quarks and Leptons, JHEP 09 (2007) 110 [arXiv:0706.1186] [SPIRES].ADSGoogle Scholar
  62. [62]
    G.-J. Ding, Fermion Mass Hierarchies and Flavor Mixing from TSymmetry, Phys. Rev. D 78 (2008) 036011 [arXiv:0803.2278] [SPIRES].ADSGoogle Scholar
  63. [63]
    P.H. Frampton and S. Matsuzaki, TPredictions of PMNS and CKM Angles, Phys. Lett. B 679 (2009) 347 [arXiv:0902.1140] [SPIRES].ADSGoogle Scholar
  64. [64]
    E. Ma, Neutrino mass matrix from S 4 symmetry, Phys. Lett. B 632 (2006) 352 [hep-ph/0508231] [SPIRES].ADSGoogle Scholar
  65.  .
    C.S. Lam, Determining Horizontal Symmetry from Neutrino Mixing, Phys. Rev. Lett. 101 (2008) 121602 [arXiv:0804.2622] [SPIRES].ADSGoogle Scholar
  66. [65]
    F. Bazzocchi and S. Morisi, S4 as a natural flavor symmetry for lepton mixing, Phys. Rev. D 80 (2009) 096005 [arXiv:0811.0345] [SPIRES].ADSGoogle Scholar
  67. [66]
    F. Bazzocchi, L. Merlo and S. Morisi, Fermion Masses and Mixings in a S4-based Model, Nucl. Phys. B 816 (2009) 204 [arXiv:0901.2086] [SPIRES].ADSGoogle Scholar
  68. [67]
    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] [SPIRES].ADSGoogle Scholar
  69. [68]
    D. Meloni, A See-Saw S 4 model for fermion masses and mixings, J. Phys. G 37 (2010) 055201 [arXiv:0911.3591] [SPIRES].ADSGoogle Scholar
  70. [69]
    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] [SPIRES].ADSGoogle Scholar
  71. [70]
    I. de Medeiros Varzielas, S.F. King and G.G. Ross, Neutrino tri-bi-maximal mixing from a non-Abelian discrete family symmetry, Phys. Lett. B 648 (2007) 201 [hep-ph/0607045] [SPIRES].ADSGoogle Scholar
  72. [71]
    C. Luhn, S. Nasri and P. Ramond, The flavor group Delta(3n 2), J. Math. Phys. 48 (2007) 073501 [hep-th/0701188] [SPIRES].MathSciNetADSGoogle Scholar
  73. [72]
    E. Ma, Near Tribimaximal Neutrino Mixing with Delta(27) Symmetry, Phys. Lett. B 660 (2008) 505 [arXiv:0709.0507] [SPIRES].ADSGoogle Scholar
  74. [73]
    W. Grimus and L. Lavoura, A Model for trimaximal lepton mixing, JHEP 09 (2008) 106 [arXiv:0809.0226] [SPIRES].ADSGoogle Scholar
  75. [74]
    C. Luhn, S. Nasri and P. Ramond, Tri-Bimaximal Neutrino Mixing and the Family Symmetry Z 7 × Z 3, Phys. Lett. B 652 (2007) 27 [arXiv:0706.2341] [SPIRES].ADSGoogle Scholar
  76. [75]
    C. Luhn, S. Nasri and P. Ramond, Simple Finite Non-Abelian Flavor Groups, J. Math. Phys. 48 (2007) 123519 [arXiv:0709.1447] [SPIRES].MathSciNetADSGoogle Scholar
  77. [76]
    L.L. Everett and A.J. Stuart, Icosahedral (A5) Family Symmetry and the Golden Ratio Prediction for Solar Neutrino Mixing, Phys. Rev. D 79 (2009) 085005 [arXiv:0812.1057] [SPIRES].ADSGoogle Scholar
  78. [77]
    R.N. Mohapatra, M.K. Parida and G. Rajasekaran, High scale mixing unification and large neutrino mixing angles, Phys. Rev. D 69 (2004) 053007 [hep-ph/0301234] [SPIRES].ADSGoogle Scholar
  79. [78]
    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] [SPIRES].ADSGoogle Scholar
  80. [79]
    E. Ma, Suitability of A 4 as a Family Symmetry in Grand Unification, Mod. Phys. Lett. A 21 (2006) 2931 [hep-ph/0607190] [SPIRES].ADSGoogle Scholar
  81. [80]
    Y. Cai and H.-B. Yu, An SO(10) GUT Model with S4 Flavor Symmetry, Phys. Rev. D 74 (2006) 115005 [hep-ph/0608022] [SPIRES].ADSGoogle Scholar
  82. [81]
    S.F. King and M. Malinsky, A 4 family symmetry and quark-lepton unification, Phys. Lett. B 645 (2007) 351 [hep-ph/0610250] [SPIRES].ADSGoogle Scholar
  83. [82]
    S. Morisi, M. Picariello and E. Torrente-Lujan, A model for fermion masses and lepton mixing in SO(10) × A4, Phys. Rev. D 75 (2007) 075015 [hep-ph/0702034] [SPIRES].ADSGoogle Scholar
  84. [83]
    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] [SPIRES].ADSGoogle Scholar
  85. [84]
    W. Grimus and H. Kuhbock, Embedding the Zee-Wolfenstein neutrino mass matrix in an SO(10)xA4 GUT scenario, Phys. Rev. D 77 (2008) 055008 [arXiv:0710.1585] [SPIRES].ADSGoogle Scholar
  86. [85]
    G. Altarelli, F. Feruglio and C. Hagedorn, A SUSY SU(5) Grand Unified Model of Tri-Bimaximal Mixing from A4, JHEP 03 (2008) 052 [arXiv:0802.0090] [SPIRES].ADSGoogle Scholar
  87. [86]
    F. Bazzocchi, S. Morisi, M. Picariello and E. Torrente-Lujan, Embedding A4 into SU(3)×U(1) flavor symmetry: Large neutrino mixing and fermion mass hierarchy in SO(10) GUT, J. Phys. G 36 (2009) 015002 [arXiv:0802.1693] [SPIRES].ADSGoogle Scholar
  88. [87]
    F. Bazzocchi, M. Frigerio and S. Morisi, Fermion masses and mixing in models with SO(10) × A 4 symmetry, Phys. Rev. D 78 (2008) 116018 [arXiv:0809.3573] [SPIRES].ADSGoogle Scholar
  89. [88]
    F. Bazzocchi, M. Frigerio and S. Morisi, Fermion masses and mixing in models with SO(10) × A 4 symmetry, Phys. Rev. D 78 (2008) 116018 [arXiv:0809.3573] [SPIRES].MATHADSGoogle Scholar
  90. [89]
    P. Ciafaloni, M. Picariello, E. Torrente-Lujan and A. Urbano, Neutrino masses and tribimaximal mixing in Minimal renormalizable SUSY SU(5) Grand Unified Model with A4 Flavor symmetry, Phys. Rev. D 79 (2009) 116010 [arXiv:0901.2236] [SPIRES].ADSGoogle Scholar
  91. [90]
    F. Bazzocchi and I. de Medeiros Varzielas, Tri-bi-maximal mixing in viable family symmetry unified model with extended seesaw, Phys. Rev. D 79 (2009) 093001 [arXiv:0902.3250] [SPIRES].ADSGoogle Scholar
  92. [91]
    S.F. King and C. Luhn, A new family symmetry for SO(10) GUTs, Nucl. Phys. B 820 (2009) 269 [arXiv:0905.1686] [SPIRES].MathSciNetADSGoogle Scholar
  93. [92]
    B. Dutta, Y. Mimura and R.N. Mohapatra, Origin of Quark-Lepton Flavor in SO(10) with Type II Seesaw, Phys. Rev. D 80 (2009) 095021 [arXiv:0910.1043] [SPIRES].ADSGoogle Scholar
  94. [93]
    B. Dutta, Y. Mimura and R.N. Mohapatra, An SO(10) Grand Unified Theory of Flavor, JHEP 05 (2010) 034 [arXiv:0911.2242] [SPIRES].MathSciNetADSGoogle Scholar
  95. [94]
    S.F. King and C. Luhn, A Supersymmetric Grand Unified Theory of Flavour with PSL(2, 7) × SO(10), Nucl.Phys. B 832 (2010) 414 [arXiv:0912.1344] [SPIRES].ADSGoogle Scholar
  96. [95]
    D.B. Kaplan, F. Lepeintre and M. Schmaltz, Flavor from strongly coupled supersymmetry, Phys. Rev. D 56 (1997) 7193 [hep-ph/9705411] [SPIRES].ADSGoogle Scholar
  97. [96]
    N. Haba and N. Okamura, Yukawa interaction from a SUSY composite model, Mod. Phys. Lett. A 13 (1998) 759 [hep-ph/9709239] [SPIRES].ADSGoogle Scholar
  98. [97]
    N. Haba, Composite model with neutrino large mixing, Phys. Rev. D 59 (1999) 035011 [hep-ph/9807552] [SPIRES].ADSGoogle Scholar
  99. [98]
    N. Arkani-Hamed and M. Schmaltz, Hierarchies without symmetries from extra dimensions, Phys. Rev. D 61 (2000) 033005 [hep-ph/9903417] [SPIRES].ADSGoogle Scholar
  100. [99]
    N. Arkani-Hamed, Y. Grossman and M. Schmaltz, Split fermions in extra dimensions and exponentially small cross-sections at future colliders, Phys. Rev. D 61 (2000) 115004 [hep-ph/9909411] [SPIRES].ADSGoogle Scholar
  101. [100]
    E.A. Mirabelli and M. Schmaltz, Yukawa hierarchies from split fermions in extra dimensions, Phys. Rev. D 61 (2000) 113011 [hep-ph/9912265] [SPIRES].ADSGoogle Scholar
  102. [101]
    Y. Grossman and M. Neubert, Neutrino masses and mixings in non-factorizable geometry, Phys. Lett. B 474 (2000) 361 [hep-ph/9912408] [SPIRES].MathSciNetADSGoogle Scholar
  103. [102]
    T. Gherghetta and A. Pomarol, Bulk fields and supersymmetry in a slice of AdS, Nucl. Phys. B 586 (2000) 141 [hep-ph/0003129] [SPIRES].MathSciNetADSGoogle Scholar
  104. [103]
    S.J. Huber and Q. Shafi, Fermion Masses, Mixings and Proton Decay in a Randall-Sundrum Model, Phys. Lett. B 498 (2001) 256 [hep-ph/0010195] [SPIRES].ADSGoogle Scholar
  105. [104]
    M. Gabella, T. Gherghetta and J. Giedt, A gravity dual and LHC study of single-sector supersymmetry breaking, Phys. Rev. D 76 (2007) 055001 [arXiv:0704.3571] [SPIRES].ADSGoogle Scholar
  106. [105]
    M.A. Luty and R.N. Mohapatra, A supersymmetric composite model of quarks and leptons, Phys. Lett. B 396 (1997) 161 [hep-ph/9611343] [SPIRES].ADSGoogle Scholar
  107. [106]
    T. Watari and T. Yanagida, Geometric origin of large lepton mixing in a higher dimensional spacetime, Phys. Lett. B 544 (2002) 167 [hep-ph/0205090] [SPIRES].ADSGoogle Scholar
  108. [107]
    T. Watari and T. Yanagida, Higher dimensional supersymmetry as an origin of the three families for quarks and leptons, Phys. Lett. B 532 (2002) 252 [hep-ph/0201086] [SPIRES].ADSGoogle Scholar
  109. [108]
    A. Adulpravitchai, A. Blum and M. Lindner, Non-Abelian Discrete Flavor Symmetries from T 2/Z N Orbifolds, JHEP 07 (2009) 053 [arXiv:0906.0468] [SPIRES].MathSciNetADSGoogle Scholar
  110. [109]
    T.J. Burrows and S.F. King, A 4 Family Symmetry from SU(5) SUSY GUTs in 6d, Nucl. Phys. B 835 (2010) 174 [arXiv:0909.1433] [SPIRES].MathSciNetADSGoogle Scholar
  111. [110]
    T. Kobayashi, S. Raby and R.-J. Zhang, Searching for realistic 4d string models with a Pati-Salam symmetry: Orbifold grand unified theories from heterotic string compactification on a Z(6) orbifold, Nucl. Phys. B 704 (2005) 3 [hep-ph/0409098] [SPIRES].MathSciNetADSGoogle Scholar
  112. [111]
    T. Kobayashi, H.P. Nilles, F. Ploger, S. Raby and M. Ratz, Stringy origin of non-Abelian discrete flavor symmetries, Nucl. Phys. B 768 (2007) 135 [hep-ph/0611020] [SPIRES].MathSciNetADSGoogle Scholar
  113. [112]
    P. Ko, T. Kobayashi, J.-h. Park and S. Raby, String-derived D 4 flavor symmetry and phenomenological implications, Phys. Rev. D 76 (2007) 035005 [arXiv:0704.2807] [SPIRES].ADSGoogle Scholar
  114. [113]
    H. Abe, K.-S. Choi, T. Kobayashi and H. Ohki, Non-Abelian Discrete Flavor Symmetries from Magnetized/Intersecting Brane Models, Nucl. Phys. B 820 (2009) 317 [arXiv:0904.2631] [SPIRES].MathSciNetADSGoogle Scholar
  115. [114]
    H. Abe, K.-S. Choi, T. Kobayashi and H. Ohki, Flavor structure from magnetic fluxes and non-Abelian Wilson lines, Phys. Rev. D 81 (2010) 126003 [arXiv:1001.1788] [SPIRES].ADSGoogle Scholar
  116. [115]
    N. Kitazawa, Dynamical generation of mu-terms and Yukawa couplings in intersecting D-brane models, JHEP 11 (2004) 044 [hep-th/0403278] [SPIRES].MathSciNetADSGoogle Scholar
  117. [116]
    N. Kitazawa, T. Kobayashi, N. Maru and N. Okada, Yukawa coupling structure in intersecting D-brane models, Eur. Phys. J. C 40 (2005) 579 [hep-th/0406115] [SPIRES].MathSciNetADSGoogle Scholar
  118. [119]
    G. Cacciapaglia, C. Csáki, C. Grojean and J. Terning, Field theory on multi-throat backgrounds, Phys. Rev. D 74 (2006) 045019 [hep-ph/0604218] [SPIRES].ADSGoogle Scholar
  119. [120]
    W.D. Goldberger and M.B. Wise, Modulus stabilization with bulk fields, Phys. Rev. Lett. 83 (1999) 4922 [hep-ph/9907447] [SPIRES].ADSGoogle Scholar
  120. [121]
    Particle Data Group collaboration, C. Amsler et al., Review of particle physics, Phys. Lett. B 667 (2008) 1 [SPIRES].ADSGoogle Scholar
  121. [122]
    P.F. Harrison, D.H. Perkins and W.G. Scott, Tri-bimaximal mixing and the neutrino oscillation data, Phys. Lett. B 530 (2002) 167 [hep-ph/0202074] [SPIRES].ADSGoogle Scholar
  122. [123]
    C. Jarlskog, A Basis Independent Formulation of the Connection Between Quark Mass Matrices, CP-violation and Experiment, Z. Phys. C 29 (1985) 491 [SPIRES].ADSGoogle Scholar
  123. [124]
    S. Abel and V.V. Khoze, Dual unified SU(5), JHEP 01 (2010) 006 [arXiv:0909.4105] [SPIRES].MathSciNetADSGoogle Scholar
  124. [125]
    D. Marti and A. Pomarol, Supersymmetric theories with compact extra dimensions in N = 1 superfields, Phys. Rev. D 64 (2001) 105025 [hep-th/0106256] [SPIRES].MathSciNetADSGoogle Scholar
  125. [165]
    T. Gherghetta, Warped models and holography, hep-ph/0601213 [SPIRES].
  126. [125]
    A. Delgado, A. Pomarol and M. Quirós, Electroweak and flavor physics in extensions of the standard model with large extra dimensions, JHEP 01 (2000) 030 [hep-ph/9911252] [SPIRES].ADSGoogle Scholar
  127. [126]
    S. Dimopoulos, S. Kachru, N. Kaloper, A.E. Lawrence and E. Silverstein, Small numbers from tunneling between brane throats, Phys. Rev. D 64 (2001) 121702 [hep-th/0104239] [SPIRES].MathSciNetADSGoogle Scholar
  128. [127]
    S. Dimopoulos, S. Kachru, N. Kaloper, A.E. Lawrence and E. Silverstein, Generating small numbers by tunneling in multi-throat compactifications, Int. J. Mod. Phys. A 19 (2004) 2657 [hep-th/0106128] [SPIRES].MathSciNetADSGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2010

Authors and Affiliations

  1. 1.Institute for Particle Physics Phenomenology and Department of Mathematical SciencesDurham UniversityDurhamU.K.

Personalised recommendations