Journal of High Energy Physics

, 2016:129 | Cite as

On a radiative origin of the Standard Model from trinification

  • José Eliel Camargo-Molina
  • António P. Morais
  • Roman Pasechnik
  • Jonas Wessén
Open Access
Regular Article - Theoretical Physics

Abstract

In this work, we present a trinification-based grand unified theory incorporating a global SU(3) family symmetry that after a spontaneous breaking leads to a left-right symmetric model. Already at the classical level, this model can accommodate the matter content and the quark Cabbibo mixing in the Standard Model (SM) with only one Yukawa coupling at the unification scale. Considering the minimal low-energy scenario with the least amount of light states, we show that the resulting effective theory enables dynamical breaking of its gauge group down to that of the SM by means of radiative corrections accounted for by the renormalisation group evolution at one loop. This result paves the way for a consistent explanation of the SM breaking scale and fermion mass hierarchies.

Keywords

GUT Effective field theories Spontaneous Symmetry Breaking Renormalization Group 

References

  1. [1]
    ATLAS collaboration, Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC, Phys. Lett. B 716 (2012) 1 [arXiv:1207.7214] [INSPIRE].
  2. [2]
    CMS collaboration, Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC, Phys. Lett. B 716 (2012) 30 [arXiv:1207.7235] [INSPIRE].
  3. [3]
    A. De Rújula, H. Georgi and S.L. Glashow, Trinification of all elementary particle forces, in Fifth Workshop on Grand Unification, K. Kang, H. Fried and F. Frampton eds., World Scientific, Singapore (1984).Google Scholar
  4. [4]
    K.S. Babu, X.-G. He and S. Pakvasa, Neutrino masses and proton decay modes in SU(3) × SU(3) × SU(3) trinification, Phys. Rev. D 33 (1986) 763 [INSPIRE].ADSGoogle Scholar
  5. [5]
    G. Lazarides and C. Panagiotakopoulos, MSSM from SUSY trinification, Phys. Lett. B 336 (1994) 190 [hep-ph/9403317] [INSPIRE].
  6. [6]
    G. Lazarides and C. Panagiotakopoulos, MSSM and large tan β from SUSY trinification, Phys. Rev. D 51 (1995) 2486 [hep-ph/9407286] [INSPIRE].
  7. [7]
    J.E. Kim, Z 3 orbifold construction of SU(3)3 GUT with \( { \sin}^2\left({\theta}_{{}^W}^0\right)=3/8 \), Phys. Lett. B 564 (2003) 35 [hep-th/0301177] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    S. Willenbrock, Triplicated trinification, Phys. Lett. B 561 (2003) 130 [hep-ph/0302168] [INSPIRE].
  9. [9]
    C.D. Carone and J.M. Conroy, Higgsless GUT breaking and trinification, Phys. Rev. D 70 (2004) 075013 [hep-ph/0407116] [INSPIRE].
  10. [10]
    J. Hetzel, Phenomenology of a left-right-symmetric model inspired by the trinification model, arXiv:1504.06739 [INSPIRE].
  11. [11]
    F. Gursey, P. Ramond and P. Sikivie, A universal gauge theory model based on E 6, Phys. Lett. B 60 (1976) 177 [INSPIRE].ADSCrossRefGoogle Scholar
  12. [12]
    Y. Achiman and B. Stech, Quark lepton symmetry and mass scales in an E 6 unified gauge model, Phys. Lett. B 77 (1978) 389 [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    Q. Shafi, E 6 as a unifying gauge symmetry, Phys. Lett. B 79 (1978) 301 [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    R. Barbieri, D.V. Nanopoulos and A. Masiero, Hierarchical fermion masses in E 6, Phys. Lett. B 104 (1981) 194 [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    B. Stech and Z. Tavartkiladze, Fermion masses and coupling unification in E 6 : life in the desert, Phys. Rev. D 70 (2004) 035002 [hep-ph/0311161] [INSPIRE].
  16. [16]
    B. Stech, Neutrino properties from E 6 × SO(3) × Z 2, Fortsch. Phys. 58 (2010) 692 [arXiv:1003.0581] [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    S.F. King, S. Moretti and R. Nevzorov, Exceptional supersymmetric Standard Model, Phys. Lett. B 634 (2006) 278 [hep-ph/0511256] [INSPIRE].
  18. [18]
    S.F. King, S. Moretti and R. Nevzorov, Theory and phenomenology of an exceptional supersymmetric Standard Model, Phys. Rev. D 73 (2006) 035009 [hep-ph/0510419] [INSPIRE].
  19. [19]
    S.F. King, S. Moretti and R. Nevzorov, Gauge coupling unification in the exceptional supersymmetric Standard Model, Phys. Lett. B 650 (2007) 57 [hep-ph/0701064] [INSPIRE].
  20. [20]
    F. Braam, A. Knochel and J. Reuter, An exceptional SSM from E 6 orbifold GUTs with intermediate LR symmetry, JHEP 06 (2010) 013 [arXiv:1001.4074] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  21. [21]
    P. Athron et al., The constrained E 6 SSM, arXiv:0810.0617 [INSPIRE].
  22. [22]
    S.F. King, R. Luo, D.J. Miller and R. Nevzorov, Leptogenesis in the exceptional supersymmetric Standard Model: flavour dependent lepton asymmetries, JHEP 12 (2008) 042 [arXiv:0806.0330] [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    P. Athron, S.F. King, D.J. Miller, S. Moretti and R. Nevzorov, Predictions of the constrained exceptional supersymmetric Standard Model, Phys. Lett. B 681 (2009) 448 [arXiv:0901.1192] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    P. Athron, S.F. King, D.J. Miller, S. Moretti and R. Nevzorov, The constrained exceptional supersymmetric Standard Model, Phys. Rev. D 80 (2009) 035009 [arXiv:0904.2169] [INSPIRE].ADSGoogle Scholar
  25. [25]
    P. Athron, S.F. King, D.J. Miller, S. Moretti and R. Nevzorov, LHC signatures of the constrained exceptional supersymmetric Standard Model, Phys. Rev. D 84 (2011) 055006 [arXiv:1102.4363] [INSPIRE].ADSGoogle Scholar
  26. [26]
    J.P. Hall et al., Novel Higgs decays and dark matter in the E 6 SSM, Phys. Rev. D 83 (2011) 075013 [arXiv:1012.5114] [INSPIRE].ADSGoogle Scholar
  27. [27]
    P. Athron, S.F. King, D.J. Miller, S. Moretti and R. Nevzorov, Constrained exceptional supersymmetric Standard Model with a Higgs near 125 GeV, Phys. Rev. D 86 (2012) 095003 [arXiv:1206.5028] [INSPIRE].ADSGoogle Scholar
  28. [28]
    R. Nevzorov, E 6 inspired supersymmetric models with exact custodial symmetry, Phys. Rev. D 87 (2013) 015029 [arXiv:1205.5967] [INSPIRE].ADSGoogle Scholar
  29. [29]
    R. Nevzorov and S. Pakvasa, Exotic Higgs decays in the E 6 inspired SUSY models, Phys. Lett. B 728 (2014) 210 [arXiv:1308.1021] [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    R. Nevzorov, Quasifixed point scenarios and the Higgs mass in the E 6 inspired supersymmetric models, Phys. Rev. D 89 (2014) 055010 [arXiv:1309.4738] [INSPIRE].ADSGoogle Scholar
  31. [31]
    R. Nevzorov and A.W. Thomas, E 6 inspired composite Higgs model, Phys. Rev. D 92 (2015) 075007 [arXiv:1507.02101] [INSPIRE].ADSGoogle Scholar
  32. [32]
    P. Athron, D. Harries, R. Nevzorov and A.G. Williams, E 6 inspired SUSY benchmarks, dark matter relic density and a 125 GeV Higgs, Phys. Lett. B 760 (2016) 19 [arXiv:1512.07040] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  33. [33]
    S.F. King and R. Nevzorov, 750 GeV diphoton resonance from singlets in an exceptional supersymmetric Standard Model, JHEP 03 (2016) 139 [arXiv:1601.07242] [INSPIRE].ADSCrossRefGoogle Scholar
  34. [34]
    P. Athron, D. Stöckinger and A. Voigt, Threshold corrections in the exceptional supersymmetric Standard Model, Phys. Rev. D 86 (2012) 095012 [arXiv:1209.1470] [INSPIRE].ADSGoogle Scholar
  35. [35]
    Y. Kawamura and T. Miura, Classification of Standard Model particles in E 6 orbifold grand unified theories, Int. J. Mod. Phys. A 28 (2013) 1350055 [arXiv:1301.7469] [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    T.G. Rizzo, Gauge kinetic mixing in the E 6 SSM, Phys. Rev. D 85 (2012) 055010 [arXiv:1201.2898] [INSPIRE].ADSGoogle Scholar
  37. [37]
    J. Reuter and D. Wiesler, Distorted mass edges at LHC from supersymmetric leptoquarks, Phys. Rev. D 84 (2011) 015012 [arXiv:1010.4215] [INSPIRE].ADSGoogle Scholar
  38. [38]
    D.J. Gross, J.A. Harvey, E.J. Martinec and R. Rohm, The heterotic string, Phys. Rev. Lett. 54 (1985) 502 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  39. [39]
    E. Cremmer, J. Scherk and J.H. Schwarz, Spontaneously broken N = 8 supergravity, Phys. Lett. B 84 (1979) 83 [INSPIRE].ADSCrossRefGoogle Scholar
  40. [40]
    E. Ma, Particle dichotomy and left-right decomposition of E 6 superstring models, Phys. Rev. D 36 (1987) 274 [INSPIRE].ADSGoogle Scholar
  41. [41]
    E. Ma, Neutrino masses in an extended gauge model with E 6 particle content, Phys. Lett. B 380 (1996) 286 [hep-ph/9507348] [INSPIRE].
  42. [42]
    J.E. Kim, Trinification with sin2 θ W = 3/8 and seesaw neutrino mass, Phys. Lett. B 591 (2004) 119 [hep-ph/0403196] [INSPIRE].
  43. [43]
    C. Cauet, H. Pas, S. Wiesenfeldt, H. Pas and S. Wiesenfeldt, Trinification, the hierarchy problem and inverse seesaw neutrino masses, Phys. Rev. D 83 (2011) 093008 [arXiv:1012.4083] [INSPIRE].ADSGoogle Scholar
  44. [44]
    J. Sayre, S. Wiesenfeldt and S. Willenbrock, Minimal trinification, Phys. Rev. D 73 (2006) 035013 [hep-ph/0601040] [INSPIRE].
  45. [45]
    C.-S. Huang, J. Jiang, T.-J. Li and W. Liao, N = 2 six-dimensional supersymmetric E 6 breaking, Phys. Lett. B 530 (2002) 218 [hep-th/0112046] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  46. [46]
    H. Georgi, Towards a grand unified theory of flavor, Nucl. Phys. B 156 (1979) 126 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  47. [47]
    B. Stech, Trinification phenomenology and the structure of Higgs bosons, JHEP 08 (2014) 139 [arXiv:1403.2714] [INSPIRE].ADSCrossRefGoogle Scholar
  48. [48]
    J. Hetzel and B. Stech, Low-energy phenomenology of trinification: an effective left-right-symmetric model, Phys. Rev. D 91 (2015) 055026 [arXiv:1502.00919] [INSPIRE].ADSGoogle Scholar
  49. [49]
    T. Lee, T. Li and C. Tsai, Hom4PS-2.0: a software package for solving polynomial systems by the polyhedral homotopy continuation method, Computing 83 (2008) 109.MathSciNetCrossRefMATHGoogle Scholar
  50. [50]
    C.P. Burgess, A Goldstone boson primer, in 11th Summer School and Symposium on Nuclear Physics (NuSS 98): Effective Theories of Matter, Seoul South Korea June 23-27 1998 [hep-ph/9812468] [INSPIRE].
  51. [51]
    C.P. Burgess, Goldstone and pseudo-Goldstone bosons in nuclear, particle and condensed matter physics, Phys. Rept. 330 (2000) 193 [hep-th/9808176] [INSPIRE].ADSCrossRefGoogle Scholar
  52. [52]
    A. Dedes, A.B. Lahanas and K. Tamvakis, Radiative electroweak symmetry breaking in the MSSM and low-energy threshold, Phys. Rev. D 53 (1996) 3793 [hep-ph/9504239] [INSPIRE].
  53. [53]
    G. Gamberini, G. Ridolfi and F. Zwirner, On radiative gauge symmetry breaking in the minimal supersymmetric model, Nucl. Phys. B 331 (1990) 331 [INSPIRE].ADSCrossRefGoogle Scholar
  54. [54]
    M. Carena, S. Pokorski and C.E.M. Wagner, On the unification of couplings in the minimal supersymmetric Standard Model, Nucl. Phys. B 406 (1993) 59 [hep-ph/9303202] [INSPIRE].
  55. [55]
    ATLAS collaboration, Search for new resonances in events with one lepton and missing transverse momentum in pp collisions at \( \sqrt{s}=13 \) TeV with the ATLAS detector, arXiv:1606.03977 [INSPIRE].
  56. [56]
    ATLAS collaboration, Search for new phenomena in the dilepton final state using proton-proton collisions at \( \sqrt{s}=13 \) TeV with the ATLAS detector, ATLAS-CONF-2015-070, CERN, Geneva Switzerland (2015).
  57. [57]
    F. Lyonnet, I. Schienbein, F. Staub and A. Wingerter, PyR@TE: renormalization group equations for general gauge theories, Comput. Phys. Commun. 185 (2014) 1130 [arXiv:1309.7030] [INSPIRE].ADSCrossRefGoogle Scholar
  58. [58]
    S. Kirkpatrick, C.D. Gelatt and M.P. Vecchi, Optimization by simulated annealing, Science 220 (1983)671 [INSPIRE].

Copyright information

© The Author(s) 2016

Authors and Affiliations

  • José Eliel Camargo-Molina
    • 1
  • António P. Morais
    • 1
    • 2
  • Roman Pasechnik
    • 1
  • Jonas Wessén
    • 1
  1. 1.Department of Astronomy and Theoretical PhysicsLund UniversityLundSweden
  2. 2.Departamento de Física, Universidade de Aveiro and CIDMAAveiroPortugal

Personalised recommendations