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Journal of High Energy Physics

, 2011:106 | Cite as

Flavored orbifold GUT — an SO(10) × S 4 model

  • Adisorn Adulpravitchai
  • Michael A. Schmidt
Article

Abstract

Orbifold grand unified theories (GUTs) solve several problems in GUT model building. Therefore, it is intriguing to investigate similar constructions in the flavor context. In this paper, we propose that a flavor symmetry might emerge due to orbifold compactification of one orbifold and broken by boundary conditions of another orbifold. The combination of the orbifold parities in gauge and flavor space determines the zero modes. We demonstrate the construction in a supersymmetric (SUSY) SO(10) × S 4 orbifold GUT model, which predicts the tribimaximal mixing at leading order in the lepton sector as well as the Cabibbo angle in the quark sector.

Keywords

Beyond Standard Model Neutrino Physics GUT 

References

  1. [1]
    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
  2. [2]
    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] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  3. [3]
    J. Berger and Y. Grossman, Model of leptons from SO(3) → A 4, JHEP 02 (2010) 071 [arXiv:0910.4392] [SPIRES].CrossRefADSGoogle Scholar
  4. [4]
    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].CrossRefMathSciNetADSGoogle Scholar
  5. [5]
    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].CrossRefMathSciNetADSGoogle Scholar
  6. [6]
    P. Ko, T. Kobayashi, J.-h. Park and S. Raby, String-derived D4 flavor symmetry and phenomenological implications, Phys. Rev. D 76 (2007) 035005 [arXiv:0704.2807] [SPIRES].ADSGoogle Scholar
  7. [7]
    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].CrossRefMathSciNetADSGoogle Scholar
  8. [8]
    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
  9. [9]
    L.J. Dixon, D. Friedan, E.J. Martinec and S.H. Shenker, The Conformal Field Theory of Orbifolds, Nucl. Phys. B 282 (1987) 13 [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  10. [10]
    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
  11. [11]
    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
  12. [12]
    G. Altarelli, F. Feruglio and Y. Lin, Tri-bimaximal neutrino mixing from orbifolding, Nucl. Phys. B 775 (2007) 31 [hep-ph/0610165] [SPIRES].CrossRefADSGoogle Scholar
  13. [13]
    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].CrossRefMathSciNetADSGoogle Scholar
  14. [14]
    Y. Kawamura, Triplet-doublet splitting, proton stability and extra dimension, Prog. Theor. Phys. 105 (2001) 999 [hep-ph/0012125] [SPIRES].CrossRefADSGoogle Scholar
  15. [15]
    T.J. Burrows and S.F. King, A 4 Family Symmetry from SU(5) SUSY GUT s in 6d, Nucl. Phys. B 835 (2010) 174 [arXiv:0909.1433] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  16. [16]
    J. Scherk and J.H. Schwarz, Spontaneous Breaking of Supersymmetry Through Dimensional Reduction, Phys. Lett. B 82 (1979) 60 [SPIRES].ADSGoogle Scholar
  17. [17]
    J. Scherk and J.H. Schwarz, How to Get Masses from Extra Dimensions, Nucl. Phys. B 153 (1979) 61 [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  18. [18]
    L.E. Ibáñez, H.P. Nilles and F. Quevedo, Orbifolds and Wilson Lines, Phys. Lett. B 187 (1987) 25 [SPIRES].ADSGoogle Scholar
  19. [19]
    N. Haba, A. Watanabe and K. Yoshioka, Twisted flavors and tri/bi-maximal neutrino mixing, Phys. Rev. Lett. 97 (2006) 041601 [hep-ph/0603116] [SPIRES].CrossRefADSGoogle Scholar
  20. [20]
    G. Seidl, Unified model of fermion masses with Wilson line flavor symmetry breaking, Phys. Rev. D 81 (2010) 025004 [arXiv:0811.3775] [SPIRES].ADSGoogle Scholar
  21. [21]
    T. Kobayashi, Y. Omura and K. Yoshioka, Flavor Symmetry Breaking and Vacuum Alignment on Orbifolds, Phys. Rev. D 78 (2008) 115006 [arXiv:0809.3064] [SPIRES].ADSGoogle Scholar
  22. [22]
    S. Pakvasa and H. Sugawara, Mass of the t Quark in SU(2) × U(1), Phys. Lett. B 82 (1979) 105 [SPIRES].ADSGoogle Scholar
  23. [23]
    Y. Yamanaka, H. Sugawara and S. Pakvasa, Permutation symmetries and the fermion mass matrix, Phys. Rev. D 25 (1982) 1895 [SPIRES].ADSGoogle Scholar
  24. [24]
    T. Brown, N. Deshpande, S. Pakvasa and H. Sugawara, CP nonconservation and rare processes in S 4 model of permutation symmetry, Phys. Lett. B 141 (1984) 95 [SPIRES].ADSGoogle Scholar
  25. [25]
    T. Brown, S. Pakvasa, H. Sugawara and Y. Yamanaka, Neutrino masses, mixing and oscillations in S 4 model of permutation symmetry, Phys. Rev. D 30 (1984) 255 [SPIRES].ADSGoogle Scholar
  26. [26]
    D.-G. Lee and R.N. Mohapatra, An SO(10) × S 4 scenario for naturally degenerate neutrinos, Phys. Lett. B 329 (1994) 463 [hep-ph/9403201] [SPIRES].ADSGoogle Scholar
  27. [27]
    E. Ma, Neutrino mass matrix from S 4 symmetry, Phys. Lett. B 632 (2006) 352 [hep-ph/0508231] [SPIRES].ADSGoogle Scholar
  28. [28]
    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].CrossRefADSGoogle Scholar
  29. [29]
    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
  30. [30]
    F. Caravaglios and S. Morisi, Gauge boson families in grand unified theories of fermion masses: E 64 xS 4, Int. J. Mod. Phys. A 22 (2007) 2469 [hep-ph/0611078] [SPIRES].MathSciNetADSGoogle Scholar
  31. [31]
    H. Zhang, Flavor S 4 × Z (2) symmetry and neutrino mixing, Phys. Lett. B 655 (2007) 132 [hep-ph/0612214] [SPIRES].ADSGoogle Scholar
  32. [32]
    Y. Koide, S 4 Flavor Symmetry Embedded into SU(3) and Lepton Masses and Mixing, JHEP 08 (2007) 086 [arXiv:0705.2275] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  33. [33]
    M.K. Parida, Intermediate left-right gauge symmetry, unification of couplings and fermion masses in SUSY SO(10) × S 4, Phys. Rev. D 78 (2008) 053004 [arXiv:0804.4571] [SPIRES].ADSGoogle Scholar
  34. [34]
    C.S. Lam, The Unique Horizontal Symmetry of Leptons, Phys. Rev. D 78 (2008) 073015 [arXiv:0809.1185] [SPIRES].ADSGoogle Scholar
  35. [35]
    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
  36. [36]
    H. Ishimori, Y. Shimizu and M. Tanimoto, S4 Flavor Symmetry of Quarks and Leptons in SU(5) GUT, Prog. Theor. Phys. 121 (2009) 769 [arXiv:0812.5031] [SPIRES].MATHCrossRefADSGoogle Scholar
  37. [37]
    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
  38. [38]
    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] [SPIRES].CrossRefADSGoogle Scholar
  39. [39]
    H. Ishimori, Y. Shimizu and M. Tanimoto, S4 Flavor Model of Quarks and Leptons, Prog. Theor. Phys. Suppl. 180 (2010) 61 [arXiv:0904.2450] [SPIRES].CrossRefADSGoogle Scholar
  40. [40]
    W. Grimus, L. Lavoura and P.O. Ludl, Is S4 the horizontal symmetry of tri-bimaximal lepton mixing?, J. Phys. G 36 (2009) 115007 [arXiv:0906.2689] [SPIRES].ADSGoogle Scholar
  41. [41]
    G.-J. Ding, Fermion Masses and Flavor Mixings in a Model with S 4 Flavor Symmetry, Nucl. Phys. B 827 (2010) 82 [arXiv:0909.2210] [SPIRES].CrossRefADSGoogle Scholar
  42. [42]
    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
  43. [43]
    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
  44. [44]
    B. Dutta, Y. Mimura and R.N. Mohapatra, An SO(10) Grand Unified Theory of Flavor, JHEP 05 (2010) 034 [arXiv:0911.2242] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  45. [45]
    R. Gatto, G. Sartori and M. Tonin, Weak Selfmasses, Cabibbo Angle and Broken SU(2) × U(2), Phys. Lett. B 28 (1968) 128 [SPIRES].ADSGoogle Scholar
  46. [46]
    R.J. Oakes, SU(2) × SU(2) breaking and the Cabibbo angle, Phys. Lett. B 29 (1969) 683 [SPIRES].ADSGoogle Scholar
  47. [47]
    E. Ponton and E. Poppitz, Casimir energy and radius stabilization in five and six dimensional orbifolds, JHEP 06 (2001) 019 [hep-ph/0105021] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  48. [48]
    W. Buchmüller, R. Catena and K. Schmidt-Hoberg, Enhanced Symmetries of Orbifolds from Moduli Stabilization, Nucl. Phys. B 821 (2009) 1 [arXiv:0902.4512] [SPIRES].CrossRefADSGoogle Scholar
  49. [49]
    T. Asaka, W. Buchm¨uller and L. Covi, Exceptional coset spaces and unification in six dimensions, Phys. Lett. B 540 (2002) 295 [hep-ph/0204358] [SPIRES].
  50. [50]
    L.J. Hall, Y. Nomura, T. Okui and D. Tucker-Smith, SO(10) unified theories in six dimensions, Phys. Rev. D 65 (2002) 035008 [hep-ph/0108071] [SPIRES].ADSGoogle Scholar
  51. [51]
    N. Arkani-Hamed, T. Gregoire and J.G. Wacker, Higher dimensional supersymmetry in 4D superspace, JHEP 03 (2002) 055 [hep-th/0101233] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  52. [52]
    A. Hebecker and J. March-Russell, The structure of GUT breaking by orbifolding, Nucl. Phys. B 625 (2002) 128 [hep-ph/0107039] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  53. [53]
    T. Asaka, W. Buchmüller and L. Covi, Bulk and brane anomalies in six dimensions, Nucl. Phys. B 648 (2003) 231 [hep-ph/0209144] [SPIRES].CrossRefADSGoogle Scholar
  54. [54]
    E.A. Mirabelli and M.E. Peskin, Transmission of supersymmetry breaking from a 4-dimensional boundary, Phys. Rev. D 58 (1998) 065002 [hep-th/9712214] [SPIRES].MathSciNetADSGoogle Scholar
  55. [55]
    T. Asaka, W. Buchmüller and L. Covi, Gauge unification in six dimensions, Phys. Lett. B 523 (2001) 199 [hep-ph/0108021] [SPIRES].ADSGoogle Scholar
  56. [56]
    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].CrossRefADSGoogle Scholar
  57. [57]
    K.R. Dienes, E. Dudas and T. Gherghetta, Extra spacetime dimensions and unification, Phys. Lett. B 436 (1998) 55 [hep-ph/9803466] [SPIRES].MathSciNetADSGoogle Scholar
  58. [58]
    K.R. Dienes, E. Dudas and T. Gherghetta, Grand unification at intermediate mass scales through extra dimensions, Nucl. Phys. B 537 (1999) 47 [hep-ph/9806292] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  59. [59]
    L. Calibbi, L. Ferretti, A. Romanino and R. Ziegler, Gauge coupling unification, the GUT scale and magic fields, Phys. Lett. B 672 (2009) 152 [arXiv:0812.0342] [SPIRES].ADSGoogle Scholar
  60. [60]
    H. Georgi and C. Jarlskog, A New Lepton-Quark Mass Relation in a Unified Theory, Phys. Lett. B 86 (1979) 297 [SPIRES].ADSGoogle Scholar
  61. [61]
    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
  62. [62]
    S.F. King, Predicting neutrino parameters from SO(3) family symmetry and quark-lepton unification, JHEP 08 (2005) 105 [hep-ph/0506297] [SPIRES].CrossRefADSGoogle Scholar
  63. [63]
    I. Masina, A maximal atmospheric mixing from a maximal CP-violating phase, Phys. Lett. B 633 (2006) 134 [hep-ph/0508031] [SPIRES].ADSGoogle Scholar
  64. [64]
    S. Antusch and S.F. King, Charged lepton corrections to neutrino mixing angles and CP phases revisited, Phys. Lett. B 631 (2005) 42 [hep-ph/0508044] [SPIRES].ADSGoogle Scholar
  65. [65]
    S. Antusch, J. Kersten, M. Lindner and M. Ratz, Running neutrino masses, mixings and CP phases: Analytical results and phenomenological consequences, Nucl. Phys. B 674 (2003) 401 [hep-ph/0305273] [SPIRES].CrossRefADSGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2011

Authors and Affiliations

  1. 1.Max Planck Institut für KernphysikHeidelbergGermany
  2. 2.Institute for Particle Physics PhenomenologyUniversity of DurhamDH1 3LEDurhamUnited Kingdom

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