A non supersymmetric SO(10) grand unified model for all the physics below M GUT

  • Guido Altarelli
  • Davide MeloniEmail author
Open Access


We present a renormalizable non supersymmetric Grand Unified SO(10) model which, at the price of a large fine tuning, is compatible with all compelling phenomenological requirements below the unification scale and thus realizes a minimal extension of the SM, unified in SO(10) and describing all known physics below M GUT. These requirements include coupling unification at a large enough scale to be compatible with the bounds on proton decay; a Yukawa sector in agreement with all the data on quark and lepton masses and mixings and with leptogenesis as the origin of the baryon asymmetry of the Universe; an axion arising from the Higgs sector of the model, suitable to solve the strong CP problem and to account for the observed amount of Dark Matter. The above constraints imposed by the data are very stringent and single out a particular breaking chain with the Pati-Salam group at an intermediate scale M I ~ 1011 GeV.


GUT Beyond Standard Model Gauge Symmetry 


  1. [1]
    E. Gildener, Gauge symmetry hierarchies, Phys. Rev. D 14 (1976) 1667 [INSPIRE].ADSGoogle Scholar
  2. [2]
    L. Maiani, Vector bosons and Higgs bosons in the Weinberg-Salam theory of weak and electromagnetic interactions, in the proceedings of the Summer School on Particle Physics, September 3–7, Gif-sur-Yvette, France (1979).Google Scholar
  3. [3]
    M. Veltman, The infrared-ultraviolet connection, Acta Phys. Polon. B 12 (1981) 437 [INSPIRE].Google Scholar
  4. [4]
    E. Witten, Dynamical Breaking of supersymmetry, Nucl. Phys. B 188 (1981) 513 [INSPIRE].ADSCrossRefGoogle Scholar
  5. [5]
    E. Witten, Mass hierarchies in supersymmetric theories, Phys. Lett. B 105 (1981) 267.MathSciNetADSCrossRefGoogle Scholar
  6. [6]
    J. Frieman, M. Turner and D. Huterer, Dark energy and the accelerating universe, Ann. Rev. Astron. Astrophys. 46 (2008) 385 [arXiv:0803.0982] [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    S. Weinberg, Anthropic bound on the cosmological constant, Phys. Rev. Lett. 59 (1987) 2607 [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    M.R. Douglas, Understanding the landscape, hep-th/0602266 [INSPIRE].
  9. [9]
    M.R. Douglas, The string landscape and low energy supersymmetry, arXiv:1204.6626 [INSPIRE].
  10. [10]
    J.-F. Cheng, D.-S. Du and C.-D. Lu, Prediction of B cDπ in the pQCD approach, Eur. Phys. J. C 45 (2006) 711 [hep-ph/0501082] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    G. Giudice and R. Rattazzi, Living dangerously with low-energy supersymmetry, Nucl. Phys. B 757 (2006) 19 [hep-ph/0606105] [INSPIRE].ADSCrossRefGoogle Scholar
  12. [12]
    G.F. Giudice, Naturally speaking: the naturalness criterion and physics at the LHC, arXiv:0801.2562 [INSPIRE].
  13. [13]
    N. Arkani-Hamed and S. Dimopoulos, Supersymmetric unification without low energy supersymmetry and signatures for fine-tuning at the LHC, JHEP 06 (2005) 073 [hep-th/0405159] [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    G. Giudice and A. Romanino, Split supersymmetry, Nucl. Phys. B 699 (2004) 65 [Erratum ibid. B 706 (2005) 65–89] [hep-ph/0406088] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    N. Arkani-Hamed, S. Dimopoulos, G. Giudice and A. Romanino, Aspects of split supersymmetry, Nucl. Phys. B 709 (2005) 3 [hep-ph/0409232] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  16. [16]
    M. Binger, Higgs boson mass in split supersymmetry at two-loops, Phys. Rev. D 73 (2006) 095001 [hep-ph/0408240] [INSPIRE].ADSGoogle Scholar
  17. [17]
    D.S. Alves, E. Izaguirre and J.G. Wacker, Higgs, binos and gluinos: split SUSY within reach, arXiv:1108.3390 [INSPIRE].
  18. [18]
    M. Cabrera, J. Casas and A. Delgado, Upper bounds on superpartner masses from upper bounds on the Higgs boson mass, Phys. Rev. Lett. 108 (2012) 021802 [arXiv:1108.3867] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    L.J. Hall and Y. Nomura, A finely-predicted Higgs boson mass from a finely-tuned weak scale, JHEP 03 (2010) 076 [arXiv:0910.2235] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    G.F. Giudice and A. Strumia, Probing high-scale and split supersymmetry with Higgs mass measurements, Nucl. Phys. B 858 (2012) 63 [arXiv:1108.6077] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    B. Bajc, A. Melfo, G. Senjanović and F. Vissani, Yukawa sector in non-supersymmetric renormalizable SO(10), Phys. Rev. D 73 (2006) 055001 [hep-ph/0510139] [INSPIRE].ADSGoogle Scholar
  22. [22]
    S. Bertolini, L. Di Luzio and M. Malinsky, Intermediate mass scales in the non-supersymmetric SO(10) grand unification: a reappraisal, Phys. Rev. D 80 (2009) 015013 [arXiv:0903.4049] [INSPIRE].ADSGoogle Scholar
  23. [23]
    S. Bertolini, L. Di Luzio and M. Malinsky, Towards a new minimal SO(10) unification, AIP Conf. Proc. 1467 (2012) 37 [arXiv:1205.5637] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    L. Di Luzio, Aspects of symmetry breaking in grand unified theories, arXiv:1110.3210 [INSPIRE].
  25. [25]
    A.S. Joshipura and K.M. Patel, Fermion masses in SO(10) models, Phys. Rev. D 83 (2011) 095002 [arXiv:1102.5148] [INSPIRE].ADSGoogle Scholar
  26. [26]
    F. Buccella, D. Falcone, C.S. Fong, E. Nardi and G. Ricciardi, Squeezing out predictions with leptogenesis from SO(10), Phys. Rev. D 86 (2012) 035012 [arXiv:1203.0829] [INSPIRE].ADSGoogle Scholar
  27. [27]
    G. Giudice, R. Rattazzi and A. Strumia, Unificaxion, Phys. Lett. B 715 (2012) 142 [arXiv:1204.5465] [INSPIRE].ADSCrossRefGoogle Scholar
  28. [28]
    S. Davidson, E. Nardi and Y. Nir, Leptogenesis, Phys. Rept. 466 (2008) 105 [arXiv:0802.2962] [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    G. Degrassi et al., Higgs mass and vacuum stability in the standard model at NNLO, JHEP 08 (2012) 098 [arXiv:1205.6497] [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    F. del Aguila and L.E. Ibáñez, Higgs bosons in SO(10) and partial unification, Nucl. Phys. B 177 (1981) 60 [INSPIRE].ADSCrossRefGoogle Scholar
  31. [31]
    J.A. Harvey, D. Reiss and P. Ramond, Mass relations and neutrino oscillations in an SO(10) model, Nucl. Phys. B 199 (1982) 223 [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    R.N. Mohapatra and G. Senjanović, The superlight axion and neutrino masses, Z. Phys. C 17 (1983) 53 [INSPIRE].ADSGoogle Scholar
  33. [33]
    R. Holman, G. Lazarides and Q. Shafi, Axions and the dark matter of the universe, Phys. Rev. D 27 (1983) 995 [INSPIRE].ADSGoogle Scholar
  34. [34]
    K. Babu and R. Mohapatra, Predictive neutrino spectrum in minimal SO(10) grand unification, Phys. Rev. Lett. 70 (1993) 2845 [hep-ph/9209215] [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    N. Deshpande, E. Keith and P.B. Pal, Implications of LEP results for SO(10) grand unification, Phys. Rev. D 46 (1993) 2261 [INSPIRE].ADSGoogle Scholar
  36. [36]
    L. Lavoura, Predicting the neutrino spectrum in minimal SO(10) grand unification, Phys. Rev. D 48 (1993) 5440 [hep-ph/9306297] [INSPIRE].ADSGoogle Scholar
  37. [37]
    R.D. Peccei and H.R. Quinn, CP conservation in the presence of pseudoparticles, Phys. Rev. Lett. 38 (1977) 1440.ADSCrossRefGoogle Scholar
  38. [38]
    R.D. Peccei and H.R. Quinn, Constraints imposed by CP conservation in the presence of pseudoparticles, Phys. Rev. D 16 (1977) 1791.ADSGoogle Scholar
  39. [39]
    S. Weinberg, A new light boson?, Phys. Rev. Lett. 40 (1978) 223.ADSCrossRefGoogle Scholar
  40. [40]
    F. Wilczek, Problem of strong P and T invariance in the presence of instantons, Phys. Rev. Lett. 40 (1978) 279.ADSCrossRefGoogle Scholar
  41. [41]
    R.D. Peccei, The strong CP problem, in CP violation, C. Jarlskog ed., Adv. Ser. Direct. High Energy Phys., World Scientific, Singapore (1989).Google Scholar
  42. [42]
    J.E. Kim, A review on axions and the strong CP problem, AIP Conf. Proc. 1200 (2010) 83 [arXiv:0909.3908] [INSPIRE].ADSCrossRefGoogle Scholar
  43. [43]
    J.E. Kim and G. Carosi, Axions and the strong CP problem, Rev. Mod. Phys. 82 (2010) 557 [arXiv:0807.3125] [INSPIRE].ADSCrossRefGoogle Scholar
  44. [44]
    W. Buchmuller, R.D. Peccei and T. Yanagida, Leptogenesis as the origin of matter, Ann. Rev. Nucl. Part. Sci. 55 (2005) 311 [hep-ph/0502169] [INSPIRE].ADSCrossRefGoogle Scholar
  45. [45]
    C.S. Fong, E. Nardi and A. Riotto, Leptogenesis in the universe, Adv. High Energy Phys. 2012 (2012) 158303 [arXiv:1301.3062] [INSPIRE].MathSciNetGoogle Scholar
  46. [46]
    W. Buchmüller, Baryogenesis, dark matter and the maximal temperature of the early universe, Acta Phys. Polon. B 43 (2012) 2153-[arXiv:1212.3554] [INSPIRE].CrossRefGoogle Scholar
  47. [47]
    B.L. Roberts, Status of the Fermilab muon (g − 2) experiment, Chin. Phys. C 34 (2010) 741 [arXiv:1001.2898] [INSPIRE].ADSCrossRefGoogle Scholar
  48. [48]
    Particle Data Group collaboration, J. Beringer et al., Review of particle physics, Phys. Rev. D 86 (2012) 010001 [INSPIRE].ADSGoogle Scholar
  49. [49]
    K. Kannike, M. Raidal, D.M. Straub and A. Strumia, Anthropic solution to the magnetic muon anomaly: the charged see-saw, JHEP 02 (2012) 106 [Erratum ibid. 1210 (2012) 136] [arXiv:1111.2551] [INSPIRE].ADSCrossRefGoogle Scholar
  50. [50]
    MEG collaboration, J. Adam et al., New constraint on the existence of the μ +e +γ decay, arXiv:1303.0754 [INSPIRE].
  51. [51]
    C.A. Baker et al., An Improved experimental limit on the electric dipole moment of the neutron, Phys. Rev. Lett. 97 (2006) 131801 [hep-ex/0602020] [INSPIRE].ADSCrossRefGoogle Scholar
  52. [52]
    S. Dimopoulos and H. Georgi, Extended survival hypothesis and fermion masses, Phys. Lett. B 140 (1984) 67 [INSPIRE].ADSCrossRefGoogle Scholar
  53. [53]
    Particle Data Group collaboration, C. Amsler et al., Review of particle physics, Phys. Lett. B 667 (2008) 1 [INSPIRE].ADSCrossRefGoogle Scholar
  54. [54]
    G. Altarelli, The QCD running coupling and its measurement, arXiv:1303.6065 [INSPIRE].
  55. [55]
    I. Koh and S. Rajpoot, Finite N = 2 extended supersymmetric field theories, Phys. Lett. B 135 (1984) 397 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  56. [56]
    D. Jones, The two loop β-function for a G 1 × G 2 gauge theory, Phys. Rev. D 25 (1982) 581 [INSPIRE].ADSGoogle Scholar
  57. [57]
  58. [58]
    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
  59. [59]
    F. Iocco, G. Mangano, G. Miele, O. Pisanti and P.D. Serpico, Primordial nucleosynthesis: from precision cosmology to fundamental physics, Phys. Rept. 472 (2009) 1 [arXiv:0809.0631] [INSPIRE].ADSCrossRefGoogle Scholar
  60. [60]
    C.S. Fong, M. Gonzalez-Garcia and E. Nardi, Leptogenesis from soft supersymmetry breaking (soft leptogenesis), Int. J. Mod. Phys. A 26 (2011) 3491 [arXiv:1107.5312] [INSPIRE].ADSCrossRefGoogle Scholar
  61. [61]
    S. Blanchet and P. Di Bari, Flavor effects on leptogenesis predictions, JCAP 03 (2007) 018 [hep-ph/0607330] [INSPIRE].ADSCrossRefGoogle Scholar
  62. [62]
    A. Abada et al., Flavour matters in leptogenesis, JHEP 09 (2006) 010 [hep-ph/0605281] [INSPIRE].ADSCrossRefGoogle Scholar
  63. [63]
    F. Buccella, D. Falcone and L. Oliver, Baryogenesis via leptogenesis from quark-lepton symmetry and a compact heavy N R spectrum, Phys. Rev. D 83 (2011) 093013 [arXiv:1006.5698] [INSPIRE].ADSGoogle Scholar
  64. [64]
    G. Fogli et al., Global analysis of neutrino masses, mixings and phases: entering the era of leptonic CP-violation searches, Phys. Rev. D 86 (2012) 013012 [arXiv:1205.5254] [INSPIRE].ADSGoogle Scholar
  65. [65]
  66. [66]
    B. Bajc, G. Senjanović and F. Vissani, Probing the nature of the seesaw in renormalizable SO(10), Phys. Rev. D 70 (2004) 093002 [hep-ph/0402140] [INSPIRE].ADSGoogle Scholar
  67. [67]
    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].ADSCrossRefGoogle Scholar
  68. [68]
    G. Fogli et al., Observables sensitive to absolute neutrino masses 2, Phys. Rev. D 78 (2008) 033010 [arXiv:0805.2517] [INSPIRE].ADSGoogle Scholar
  69. [69]
    E. Ma, S. Sarkar and U. Sarkar, Scale of SU(2)(R) symmetry breaking and leptogenesis, Phys. Lett. B 458 (1999) 73 [hep-ph/9812276] [INSPIRE].ADSCrossRefGoogle Scholar
  70. [70]
    S. Carlier, J. Frere and F. Ling, Gauge dilution and leptogenesis, Phys. Rev. D 60 (1999) 096003 [hep-ph/9903300] [INSPIRE].ADSGoogle Scholar
  71. [71]
    N. Cosme, Leptogenesis, neutrino masses and gauge unification, JHEP 08 (2004) 027 [hep-ph/0403209] [INSPIRE].ADSCrossRefGoogle Scholar
  72. [72]
  73. [73]
    Planck collaboration, P. Ade et al., Planck 2013 results. XVI. Cosmological parameters, arXiv:1303.5076 [INSPIRE].
  74. [74]
    Planck collaboration, P. Ade et al., Planck 2013 results. XXII. Constraints on inflation, arXiv:1303.5082 [INSPIRE].
  75. [75]
    A.D. Linde, Axions in inflationary cosmology, Phys. Lett. B 259 (1991) 38 [INSPIRE].ADSCrossRefGoogle Scholar
  76. [76]
    S. Folkerts, C. Germani and J. Redondo, Axion dark matter and Planck favor non-minimal couplings to gravity, arXiv:1304.7270 [INSPIRE].
  77. [77]
    K.S. Jeong and F. Takahashi, Suppressing isocurvature perturbations of QCD axion dark matter, arXiv:1304.8131 [INSPIRE].

Copyright information

© SISSA 2013

Authors and Affiliations

  1. 1.Dipartimento di Matematica e FisicaUniversità di Roma Tre and INFN — Sezione di Roma TreRomeItaly
  2. 2.CERN, Department of Physics, Theory DivisionGeneva 23Switzerland

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