The minimal adjoint-SU(5) × Z 4 GUT model

  • D. Emmanuel-CostaEmail author
  • C. Simões
  • M. Tórtola


An extension of the adjoint SU(5) model with a flavour symmetry based on the Z4 group is investigated. The Z4 symmetry is introduced with the aim of leading the up- and down-quark mass matrices to the Nearest-Neighbour-Interaction form. As a consequence of the discrete symmetry embedded in the SU(5) gauge group, the charged lepton mass matrix also gets the same form. Within this model, light neutrinos get their masses through type-I, type-III and one-loop radiative seesaw mechanisms, implemented, respectively, via a singlet, a triplet and an octet from the adjoint fermionic 24 fields. It is demonstrated that the neutrino phenomenology forces the introduction of at least three 24 fermionic multiplets. The symmetry SU(5) × Z4 allows only two viable zero textures for the effective neutrino mass matrix. It is showed that one texture is only compatible with normal hierarchy and the other with inverted hierarchy in the light neutrino mass spectrum. Finally, it is also demonstrated that Z4 freezes out the possibility of proton decay through exchange of coloured Higgs triplets at tree-level.


Neutrino Physics GUT Discrete and Finite Symmetries 


  1. [1]
    H. Georgi and S. Glashow, Unity of All Elementary Particle Forces, Phys. Rev. Lett. 32 (1974) 438 [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    H. Georgi, The State of the Art-Gauge Theories. (Talk), AIP Conf. Proc. 23 (1975) 575.ADSCrossRefGoogle Scholar
  3. [3]
    H. Fritzsch and P. Minkowski, Unified Interactions of Leptons and Hadrons, Annals Phys. 93 (1975) 193 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  4. [4]
    P. Nath and P. Fileviez Pérez, Proton stability in grand unified theories, in strings and in branes, Phys. Rept. 441 (2007) 191 [hep-ph/0601023] [INSPIRE].ADSCrossRefGoogle Scholar
  5. [5]
    B. Bajc, P. Fileviez Pérez and G. Senjanović, Proton decay in minimal supersymmetric SU(5), Phys. Rev. D 66 (2002) 075005 [hep-ph/0204311] [INSPIRE].ADSGoogle Scholar
  6. [6]
    B. Bajc, P. Fileviez Pérez and G. Senjanović, Minimal supersymmetric SU(5) theory and proton decay: Where do we stand?, hep-ph/0210374 [INSPIRE].
  7. [7]
    D. Emmanuel-Costa and S. Wiesenfeldt, Proton decay in a consistent supersymmetric SU(5) GUT model, Nucl. Phys. B 661 (2003) 62 [hep-ph/0302272] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    P. Fileviez Pérez, Renormalizable adjoint SU(5), Phys. Lett. B 654 (2007) 189 [hep-ph/0702287] [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    P. Fileviez Pérez, H. Iminniyaz and G. Rodrigo, Proton Stability, Dark Matter and Light Color Octet Scalars in Adjoint SU(5) Unification, Phys. Rev. D 78 (2008) 015013 [arXiv:0803.4156] [INSPIRE].ADSGoogle Scholar
  10. [10]
    P. Frampton, S. Nandi and J. Scanio, Estimate of Flavor Number From SU(5) Grand Unification, Phys. Lett. B 85 (1979) 225 [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    H. Georgi and C. Jarlskog, A New Lepton-Quark Mass Relation in a Unified Theory, Phys. Lett. B 86 (1979) 297 [INSPIRE].ADSCrossRefGoogle Scholar
  12. [12]
    P. Langacker, Grand Unified Theories and Proton Decay, Phys. Rept. 72 (1981) 185 [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    G. Branco, C. Geng, R. Marshak and P. Xue, Phenomenological Clues for Discrete Symmetries in Superstring Theories, Phys. Rev. D 36 (1987) 928 [INSPIRE].ADSGoogle Scholar
  14. [14]
    K.S. Babu and J. Kubo, Dihedral families of quarks, leptons and Higgses, Phys. Rev. D 71 (2005) 056006 [hep-ph/0411226] [INSPIRE].ADSGoogle Scholar
  15. [15]
    W. Grimus, A.S. Joshipura, L. Lavoura and M. Tanimoto, Symmetry realization of texture zeros, Eur. Phys. J. C 36 (2004) 227 [hep-ph/0405016] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    C.I. Low, Abelian family symmetries and the simplest models that give θ 13 = 0 in the neutrino mixing matrix, Phys. Rev. D 71 (2005) 073007 [hep-ph/0501251] [INSPIRE].ADSGoogle Scholar
  17. [17]
    P. Ferreira and J.P. Silva, Abelian symmetries in the two-Higgs-doublet model with fermions, Phys. Rev. D 83 (2011) 065026 [arXiv:1012.2874] [INSPIRE].ADSGoogle Scholar
  18. [18]
    F. Gonzalez Canales and A. Mondragon, The S 3 symmetry: Flavour and texture zeroes, J. Phys. Conf. Ser. 287 (2011) 012015 [arXiv:1101.3807] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    G. Branco, D. Emmanuel-Costa and R. Gonzalez Felipe, Texture zeros and weak basis transformations, Phys. Lett. B 477 (2000) 147 [hep-ph/9911418] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    G. Branco, D. Emmanuel-Costa, R. Gonzalez Felipe and H. Serodio, Weak Basis Transformations and Texture Zeros in the Leptonic Sector, Phys. Lett. B 670 (2009) 340 [arXiv:0711.1613] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    D. Emmanuel-Costa and C. Simoes, Reconstruction of Quark Mass Matrices with Weak Basis Texture Zeroes from Experimental Input, Phys. Rev. D 79 (2009) 073006 [arXiv:0903.0564] [INSPIRE].ADSGoogle Scholar
  22. [22]
    H. Fritzsch, Weak Interaction Mixing in the Six-Quark Theory, Phys. Lett. B 73 (1978) 317 [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    H. Fritzsch, Quark Masses and Flavor Mixing, Nucl. Phys. B 155 (1979) 189 [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    G. Branco, D. Emmanuel-Costa and C. Simões, Nearest-Neighbour Interaction from an Abelian Symmetry and Deviations from Hermiticity, Phys. Lett. B 690 (2010) 62 [arXiv:1001.5065] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    N. Cabibbo, Unitary Symmetry and Leptonic Decays, Phys. Rev. Lett. 10 (1963) 531 [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    M. Kobayashi and T. Maskawa, CP Violation in the Renormalizable Theory of Weak Interaction, Prog. Theor. Phys. 49 (1973) 652 [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    D. Emmanuel-Costa and C. Simões, Nearest-Neighbour-Interactions from a minimal discrete flavour symmetry within SU(5) Grand Unification, Phys. Rev. D 85 (2012) 016003 [arXiv:1102.3729] [INSPIRE].ADSGoogle Scholar
  28. [28]
    L.M. Krauss and F. Wilczek, Discrete Gauge Symmetry in Continuum Theories, Phys. Rev. Lett. 62 (1989) 1221 [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    I.K. Cooper, S.F. King and C. Luhn, SUSY SU(5) with singlet plus adjoint matter and A4 family symmetry, Phys. Lett. B 690 (2010) 396 [arXiv:1004.3243] [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    G.-J. Ding, SUSY adjoint SU(5) grand unified model with S 4 flavor symmetry, Nucl. Phys. B 846 (2011) 394 [arXiv:1006.4800] [INSPIRE].ADSCrossRefGoogle Scholar
  31. [31]
    I. Doršner and P. Fileviez Pérez, Upper Bound on the Mass of the Type III Seesaw Triplet in an SU(5) Model, JHEP 06 (2007) 029 [hep-ph/0612216] [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    P. Fileviez Pérez, Supersymmetric Adjoint SU(5), Phys. Rev. D 76 (2007) 071701 [arXiv:0705.3589] [INSPIRE].Google Scholar
  33. [33]
    S. Blanchet and P. Fileviez Pérez, Baryogenesis via Leptogenesis in Adjoint SU(5), JCAP 08 (2008) 037 [arXiv:0807.3740] [INSPIRE].ADSCrossRefGoogle Scholar
  34. [34]
    K. Kannike and D.V. Zhuridov, New Solution for Neutrino Masses and Leptogenesis in Adjoint SU(5), JHEP 07 (2011) 102 [arXiv:1105.4546] [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    P. Minkowski, μeγ at a Rate of One Out of 1-Billion Muon Decays?, Phys. Lett. B 67 (1977) 421 [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    T. Yanagida, Horizontal symmetry and masses of neutrinos, in Proceedings of The Workshop on Unified Theory and Baryon Number in the Universe, KEK, Tsukuba, Japan (1979), Conf. Proc. C7902131 (1979) 95 [INSPIRE].
  37. [37]
    M. Gell-Mann, P. Ramond, and R. Slansky, Complex spinors and unified theories, to be published in Supergravity, P. van Nieuwenhuizen & D.Z. Freedman eds., North Holland Publ. Co., (1979), Conf. Proc. C790927 (1979) 315 [arXiv:1306.4669] [INSPIRE].
  38. [38]
    R.N. Mohapatra and G. Senjanović, Neutrino Mass and Spontaneous Parity Violation, Phys. Rev. Lett. 44 (1980) 912 [INSPIRE].ADSCrossRefGoogle Scholar
  39. [39]
    J. Schechter and J. Valle, Neutrino Masses in SU(2) × U(1) Theories, Phys. Rev. D 22 (1980) 2227 [INSPIRE].ADSGoogle Scholar
  40. [40]
    R. Foot, H. Lew, X. He and G.C. Joshi, Seesaw Neutrino Masses Induced by a Triplet of Leptons, Z. Phys. C 44 (1989) 441 [INSPIRE].Google Scholar
  41. [41]
    E. Ma, Pathways to naturally small neutrino masses, Phys. Rev. Lett. 81 (1998) 1171 [hep-ph/9805219] [INSPIRE].ADSCrossRefGoogle Scholar
  42. [42]
    A. Zee, A Theory of Lepton Number Violation, Neutrino Majorana Mass and Oscillation, Phys. Lett. B 93 (1980) 389 [Erratum ibid. B 95 (1980) 461] [INSPIRE].ADSCrossRefGoogle Scholar
  43. [43]
    L. Wolfenstein, A Theoretical Pattern for Neutrino Oscillations, Nucl. Phys. B 175 (1980) 93 [INSPIRE].ADSCrossRefGoogle Scholar
  44. [44]
    E. Ma, Verifiable radiative seesaw mechanism of neutrino mass and dark matter, Phys. Rev. D 73 (2006) 077301 [hep-ph/0601225] [INSPIRE].ADSGoogle Scholar
  45. [45]
    P. Fileviez Pérez and M.B. Wise, On the Origin of Neutrino Masses, Phys. Rev. D 80 (2009) 053006 [arXiv:0906.2950] [INSPIRE].ADSGoogle Scholar
  46. [46]
    I. Doršner, S. Fajfer and N. Košnik, Heavy and light scalar leptoquarks in proton decay, Phys. Rev. D 86 (2012) 015013 [arXiv:1204.0674] [INSPIRE].ADSGoogle Scholar
  47. [47]
    I. Doršsner, S. Fajfer, J.F. Kamenik and N. Košnik, Light Colored Scalar as Messenger of Up-Quark Flavor Dynamics in Grand Unified Theories, Phys. Rev. D 82 (2010) 094015 [arXiv:1007.2604] [INSPIRE].ADSGoogle Scholar
  48. [48]
    H. Georgi and A. Pais, CP-Violation as a Quantum Effect, Phys. Rev. D 10 (1974) 1246 [INSPIRE].ADSGoogle Scholar
  49. [49]
    S. Weinberg, Approximate symmetries and pseudoGoldstone bosons, Phys. Rev. Lett. 29 (1972) 1698 [INSPIRE].ADSCrossRefGoogle Scholar
  50. [50]
    Particle Data Group collaboration, J. Beringer et al., Review of Particle Physics (RPP), Phys. Rev. D 86 (2012) 010001 [INSPIRE].ADSGoogle Scholar
  51. [51]
    A. Giveon, L.J. Hall and U. Sarid, SU(5) unification revisited, Phys. Lett. B 271 (1991) 138 [INSPIRE].ADSCrossRefGoogle Scholar
  52. [52]
    D. Emmanuel-Costa, E.T. Franco and R. González Felipe, SU(5) × SU(5) unification revisited, JHEP 08 (2011) 017 [arXiv:1104.2046] [INSPIRE].ADSCrossRefGoogle Scholar
  53. [53]
    J. Hewett et al., Fundamental Physics at the Intensity Frontier, arXiv:1205.2671 [INSPIRE].
  54. [54]
    D. Forero, M. Tortola and J. Valle, Global status of neutrino oscillation parameters after Neutrino-2012, Phys. Rev. D 86 (2012) 073012 [arXiv:1205.4018] [INSPIRE].ADSGoogle Scholar
  55. [55]
    P.H. Frampton, S.L. Glashow and D. Marfatia, Zeroes of the neutrino mass matrix, Phys. Lett. B 536 (2002) 79 [hep-ph/0201008] [INSPIRE].ADSCrossRefGoogle Scholar
  56. [56]
    B.R. Desai, D. Roy and A.R. Vaucher, Three neutrino mass matrices with two texture zeros, Mod. Phys. Lett. A 18 (2003) 1355 [hep-ph/0209035] [INSPIRE].ADSCrossRefGoogle Scholar
  57. [57]
    S. Dev, S. Kumar, S. Verma and S. Gupta, Phenomenology of two-texture zero neutrino mass matrices, Phys. Rev. D 76 (2007) 013002 [hep-ph/0612102] [INSPIRE].ADSGoogle Scholar
  58. [58]
    W.-l. Guo and Z.-z. Xing, Implications of the KamLAND measurement on the lepton flavor mixing matrix and the neutrino mass matrix, Phys. Rev. D 67 (2003) 053002 [hep-ph/0212142] [INSPIRE].ADSGoogle Scholar
  59. [59]
    R. Johnson, S. Ranfone and J. Schechter, The Neutrino Seesaw in SO(10), Phys. Lett. B 179 (1986) 355 [INSPIRE].ADSCrossRefGoogle Scholar
  60. [60]
    S.L. Glashow, A novel neutrino mass hierarchy, Phys. Lett. B 256 (1991) 255 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  61. [61]
    M. Fukugita and T. Yanagida, Cripple seesaw mechanism, Phys. Rev. Lett. 66 (1991) 2705 [INSPIRE].ADSCrossRefGoogle Scholar
  62. [62]
    T. Allen, R. Johnson, S. Ranfone, J. Schechter and J. Valle, Simpsons neutrino and the singular seesaw, Mod. Phys. Lett. A 6 (1991) 1967 [INSPIRE].ADSCrossRefGoogle Scholar
  63. [63]
    E. Chun, C. Kim and U. Lee, Three neutrino Δm 2 scales and singular seesaw mechanism, Phys. Rev. D 58 (1998) 093003 [hep-ph/9802209] [INSPIRE].ADSGoogle Scholar
  64. [64]
    C. Liu and J.-H. Song, Four light neutrinos in singular seesaw mechanism with Abelian flavor symmetry, Phys. Rev. D 60 (1999) 036002 [hep-ph/9812381] [INSPIRE].ADSGoogle Scholar
  65. [65]
    Y. Chikira, N. Haba and Y. Mimura, The singular seesaw mechanism with hierarchical Dirac neutrino mass, Eur. Phys. J. C 16 (2000) 701 [hep-ph/9808254] [INSPIRE].ADSCrossRefGoogle Scholar
  66. [66]
    G.J. Stephenson, J.T. Goldman, B. McKellar and M. Garbutt, Large mixing from small: PseudoDirac neutrinos and the singular seesaw, Int. J. Mod. Phys. A 20 (2005) 6373 [hep-ph/0404015] [INSPIRE].ADSCrossRefGoogle Scholar
  67. [67]
    C. Simões, The adjoint SU(5) constrained by a Z 4 flavour symmetry, J. Phys. Conf. Ser. 447 (2013) 012041 [INSPIRE].ADSCrossRefGoogle Scholar
  68. [68]
    DAYA-BAY collaboration, F. An et al., Observation of electron-antineutrino disappearance at Daya Bay, Phys. Rev. Lett. 108 (2012) 171803 [arXiv:1203.1669] [INSPIRE].ADSCrossRefGoogle Scholar
  69. [69]
    B. Pontecorvo, Mesonium and anti-mesonium, Sov. Phys. JETP 6 (1957) 429 [INSPIRE].ADSGoogle Scholar
  70. [70]
    B. Pontecorvo, Inverse beta processes and nonconservation of lepton charge, Sov. Phys. JETP 7 (1958) 172 [INSPIRE].Google Scholar
  71. [71]
    Z. Maki, M. Nakagawa and S. Sakata, Remarks on the unified model of elementary particles, Prog. Theor. Phys. 28 (1962) 870 [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  72. [72]
    G.C. Branco and M. Rebelo, Building the full PMNS Matrix from six independent Majorana-type phases, Phys. Rev. D 79 (2009) 013001 [arXiv:0809.2799] [INSPIRE].ADSGoogle Scholar
  73. [73]
    G. Branco, R.G. Felipe and F. Joaquim, Leptonic CP-violation, Rev. Mod. Phys. 84 (2012) 515 [arXiv:1111.5332] [INSPIRE].ADSCrossRefGoogle Scholar
  74. [74]
    H. Fusaoka and Y. Koide, Updated estimate of running quark masses, Phys. Rev. D 57 (1998) 3986 [hep-ph/9712201] [INSPIRE].ADSGoogle Scholar
  75. [75]
    Z.-z. Xing, H. Zhang and S. Zhou, Updated Values of Running Quark and Lepton Masses, Phys. Rev. D 77 (2008) 113016 [arXiv:0712.1419] [INSPIRE].ADSGoogle Scholar
  76. [76]
    A. Giuliani and A. Poves, Neutrinoless Double-Beta Decay, Adv. High Energy Phys. 2012 (2012) 857016.Google Scholar
  77. [77]
    Planck collaboration, P. Ade et al., Planck 2013 results. XVI. Cosmological parameters, arXiv:1303.5076 [INSPIRE].
  78. [78]
    J. Lesgourgues and S. Pastor, Neutrino mass from Cosmology, Adv. High Energy Phys. 2012 (2012) 608515 [arXiv:1212.6154] [INSPIRE].Google Scholar
  79. [79]
    E. Otten and C. Weinheimer, Neutrino mass limit from tritium beta decay, Rept. Prog. Phys. 71 (2008) 086201 [arXiv:0909.2104] [INSPIRE].ADSCrossRefGoogle Scholar
  80. [80]
    M. Fischler, Young tableau Methods for Kronecker Products of Representations of the Classical Groups, J. Math. Phys. 22 (1981) 637 [INSPIRE].MathSciNetADSCrossRefzbMATHGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2013

Authors and Affiliations

  1. 1.Departamento de Física and Centro de Física Teórica de Partículas (CFTP)Instituto Superior Técnico (IST), Universidade de LisboaLisboaPortugal
  2. 2.AHEP Group, Instituto de Física Corpuscular - C.S.I.C./Universitat de València, Edificio Institutos de PaternaValenciaSpain

Personalised recommendations