Advertisement

Journal of High Energy Physics

, 2015:155 | Cite as

Mass-splitting between haves and have-nots — symmetry vs. Grand Unified Theory

  • Keisuke Harigaya
  • Masahiro Ibe
  • Motoo SuzukiEmail author
Open Access
Regular Article - Theoretical Physics

Abstract

We revisit the long-standing problem of supersymmetric grand unified theory (GUT), the doublet-triplet splitting problem. We discuss whether symmetry which controls the μ term in the minimal supersymmetric standard model is compatible with GUT. We find that the symmetry must be broken at the GUT scale. A similar argument also shows that the R symmetry, which is important for low energy supersymmetry, must be broken down to a Z 2R symmetry at the GUT scale. We propose a new prescription to achieve the doublet-triplet splitting by symmetry. There, the symmetry which controls the μ term is spontaneously broken at the GUT scale by order parameters which are charged under other symmetries. Bilinear terms of triplet Higgses are charged under the other symmetries, while those of doublet Higgses are not. Then triplet Higgses directly couple to the order parameters and hence obtain GUT scale masses, while doublet Higgses obtain suppressed masses. The broken R symmetry can be also effectively preserved by a similar prescription. As a demonstration, we construct an SU(5) × SU(5) GUT model. We also comment on unification of yukawa couplings.

Keywords

Beyond Standard Model Supersymmetric Standard Model GUT Discrete and Finite Symmetries 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    L. Maiani, in proceedings of Summer School on Particle Physics, Paris, France (1979).Google Scholar
  2. [2]
    M.J.G. Veltman, The Infrared-Ultraviolet Connection, Acta Phys. Polon. B 12 (1981) 437 [INSPIRE].Google Scholar
  3. [3]
    E. Witten, Mass Hierarchies in Supersymmetric Theories, Phys. Lett. B 105 (1981) 267 [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    R.K. Kaul, Gauge Hierarchy in a Supersymmetric Model, Phys. Lett. B 109 (1982) 19 [INSPIRE].ADSCrossRefGoogle Scholar
  5. [5]
    H. Georgi and S.L. Glashow, Unity of All Elementary Particle Forces, Phys. Rev. Lett. 32 (1974) 438 [INSPIRE].ADSCrossRefGoogle Scholar
  6. [6]
    CMS collaboration, Search for new physics in the multijet and missing transverse momentum final state in proton-proton collisions at \( \sqrt{s}=8 \) TeV, JHEP 06 (2014) 055 [arXiv:1402.4770] [INSPIRE].
  7. [7]
    ATLAS collaboration, Search for squarks and gluinos with the ATLAS detector in final states with jets and missing transverse momentum using \( \sqrt{s}=8 \) TeV proton-proton collision data, JHEP 09 (2014) 176 [arXiv:1405.7875] [INSPIRE].
  8. [8]
    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].
  9. [9]
    ATLAS collaboration, Measurement of the Higgs boson mass from the Hγγ and HZZ * →4ℓ channels with the ATLAS detector using 25fb −1 of pp collision data, Phys. Rev. D 90 (2014) 052004 [arXiv:1406.3827] [INSPIRE].
  10. [10]
    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].
  11. [11]
    CMS collaboration, Measurement of the properties of a Higgs boson in the four-lepton final state, Phys. Rev. D 89 (2014) 092007 [arXiv:1312.5353] [INSPIRE].
  12. [12]
    CMS collaboration, Observation of the diphoton decay of the Higgs boson and measurement of its properties, Eur. Phys. J. C 74 (2014) 3076 [arXiv:1407.0558] [INSPIRE].
  13. [13]
    S. Dimopoulos and H. Georgi, Softly Broken Supersymmetry and SU(5), Nucl. Phys. B 193 (1981) 150 [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    N. Sakai, Naturalness in Supersymmetric Guts, Z. Phys. C 11 (1981) 153 [INSPIRE].ADSGoogle Scholar
  15. [15]
    A. Masiero, D.V. Nanopoulos, K. Tamvakis and T. Yanagida, Naturally Massless Higgs Doublets in Supersymmetric SU(5), Phys. Lett. B 115 (1982) 380 [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    B. Grinstein, A Supersymmetric SU(5) Gauge Theory with No Gauge Hierarchy Problem, Nucl. Phys. B 206 (1982) 387 [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    S. Dimopoulos and F. Wilczek, Incomplete multiplets in supersymmetric unified models, NSF-ITP-82-07 (1981).
  18. [18]
    T. Yanagida, Naturally light Higgs doublets in the supersymmetric grand unified theories with dynamical symmetry breaking, Phys. Lett. B 344 (1995) 211 [hep-ph/9409329] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    Y. Kawamura, Triplet doublet splitting, proton stability and extra dimension, Prog. Theor. Phys. 105 (2001) 999 [hep-ph/0012125] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    L.J. Hall and Y. Nomura, Gauge unification in higher dimensions, Phys. Rev. D 64 (2001) 055003 [hep-ph/0103125] [INSPIRE].ADSGoogle Scholar
  21. [21]
    K.I. Izawa and T. Yanagida, R invariant natural unification, Prog. Theor. Phys. 97 (1997) 913 [hep-ph/9703350] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    K. Inoue, M. Kawasaki, M. Yamaguchi and T. Yanagida, Vanishing squark and slepton masses in a class of supergravity models, Phys. Rev. D 45 (1992) 328 [INSPIRE].ADSGoogle Scholar
  23. [23]
    J.A. Casas and C. Muñoz, A natural solution to the μ problem, Phys. Lett. B 306 (1993) 288 [hep-ph/9302227] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    J.E. Kim and H.P. Nilles, The μ Problem and the Strong CP Problem, Phys. Lett. B 138 (1984) 150 [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    M.W. Goodman and E. Witten, Global Symmetries in Four-dimensions and Higher Dimensions, Nucl. Phys. B 271 (1986) 21 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  26. [26]
    E. Witten, Deconstruction, G 2 holonomy and doublet triplet splitting, hep-ph/0201018 [INSPIRE].
  27. [27]
    M. Fallbacher, M. Ratz and P.K.S. Vaudrevange, No-go theorems for R symmetries in four-dimensional GUTs, Phys. Lett. B 705 (2011) 503 [arXiv:1109.4797] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  28. [28]
    K.I. Izawa and T. Yanagida, R invariant unification with dynamical Higgs multiplets, Prog. Theor. Phys. 99 (1998) 423 [hep-ph/9710218] [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    R. Kitano and N. Okada, Dynamical doublet-triplet Higgs mass splitting, Phys. Rev. D 64 (2001) 055010 [hep-ph/0105220] [INSPIRE].ADSGoogle Scholar
  30. [30]
    S. Antusch, I. de Medeiros Varzielas, V. Maurer, C. Sluka and M. Spinrath, Towards predictive flavour models in SUSY SU(5) GUTs with doublet-triplet splitting, JHEP 09 (2014) 141 [arXiv:1405.6962] [INSPIRE].ADSCrossRefGoogle Scholar
  31. [31]
    M. Dine, Y. Nir and Y. Shadmi, Product groups, discrete symmetries and grand unification, Phys. Rev. D 66 (2002) 115001 [hep-ph/0206268] [INSPIRE].ADSGoogle Scholar
  32. [32]
    G.F. Giudice and A. Masiero, A Natural Solution to the μ Problem in Supergravity Theories, Phys. Lett. B 206 (1988) 480 [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    M. Ibe, T. Moroi and T.T. Yanagida, Possible Signals of Wino LSP at the Large Hadron Collider, Phys. Lett. B 644 (2007) 355 [hep-ph/0610277] [INSPIRE].ADSCrossRefGoogle Scholar
  34. [34]
    M. Ibe and T.T. Yanagida, The Lightest Higgs Boson Mass in Pure Gravity Mediation Model, Phys. Lett. B 709 (2012) 374 [arXiv:1112.2462] [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    M. Ibe, S. Matsumoto and T.T. Yanagida, Pure Gravity Mediation with m 3/2 = 10100 TeV, Phys. Rev. D 85 (2012) 095011 [arXiv:1202.2253] [INSPIRE].ADSGoogle Scholar
  36. [36]
    B. Bhattacherjee, B. Feldstein, M. Ibe, S. Matsumoto and T.T. Yanagida, Pure gravity mediation of supersymmetry breaking at the Large Hadron Collider, Phys. Rev. D 87 (2013) 015028 [arXiv:1207.5453] [INSPIRE].ADSGoogle Scholar
  37. [37]
    G.F. Giudice, M.A. Luty, H. Murayama and R. Rattazzi, Gaugino mass without singlets, JHEP 12 (1998) 027 [hep-ph/9810442] [INSPIRE].ADSCrossRefGoogle Scholar
  38. [38]
    L. Randall and R. Sundrum, Out of this world supersymmetry breaking, Nucl. Phys. B 557 (1999) 79 [hep-th/9810155] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  39. [39]
    M. Dine and D. MacIntire, Supersymmetry, naturalness and dynamical supersymmetry breaking, Phys. Rev. D 46 (1992) 2594 [hep-ph/9205227] [INSPIRE].ADSGoogle Scholar
  40. [40]
    J.A. Bagger, T. Moroi and E. Poppitz, Anomaly mediation in supergravity theories, JHEP 04 (2000) 009 [hep-th/9911029] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  41. [41]
    F. D’Eramo, J. Thaler and Z. Thomas, Anomaly Mediation from Unbroken Supergravity, JHEP 09 (2013) 125 [arXiv:1307.3251] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  42. [42]
    K. Harigaya and M. Ibe, Anomaly Mediated Gaugino Mass and Path-Integral Measure, Phys. Rev. D 90 (2014) 085028 [arXiv:1409.5029] [INSPIRE].ADSGoogle Scholar
  43. [43]
    G.D. Coughlan, W. Fischler, E.W. Kolb, S. Raby and G.G. Ross, Cosmological Problems for the Polonyi Potential, Phys. Lett. B 131 (1983) 59 [INSPIRE].ADSCrossRefGoogle Scholar
  44. [44]
    M. Ibe, Y. Shinbara and T.T. Yanagida, The Polonyi Problem and Upper bound on Inflation Scale in Supergravity, Phys. Lett. B 639 (2006) 534 [hep-ph/0605252] [INSPIRE].ADSCrossRefGoogle Scholar
  45. [45]
    K. Harigaya, M. Ibe, K. Schmitz and T.T. Yanagida, A Simple Solution to the Polonyi Problem in Gravity Mediation, Phys. Lett. B 721 (2013) 86 [arXiv:1301.3685] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  46. [46]
    R. Barbieri, G.R. Dvali and A. Strumia, Strings versus supersymmetric GUTs: Can they be reconciled?, Phys. Lett. B 333 (1994) 79 [hep-ph/9404278] [INSPIRE].ADSCrossRefGoogle Scholar
  47. [47]
    N. Sakai and T. Yanagida, Proton Decay in a Class of Supersymmetric Grand Unified Models, Nucl. Phys. B 197 (1982) 533 [INSPIRE].ADSCrossRefGoogle Scholar
  48. [48]
    G.F. Giudice and A. Romanino, Split supersymmetry, Nucl. Phys. B 699 (2004) 65 [Erratum ibid. B 706 (2005) 65] [hep-ph/0406088] [INSPIRE].
  49. [49]
    J.R. Ellis, M.K. Gaillard, D.V. Nanopoulos and S. Rudaz, Uncertainties in the Proton Lifetime, Nucl. Phys. B 176 (1980) 61 [INSPIRE].ADSCrossRefGoogle Scholar
  50. [50]
    H. Georgi, H.R. Quinn and S. Weinberg, Hierarchy of Interactions in Unified Gauge Theories, Phys. Rev. Lett. 33 (1974) 451 [INSPIRE].ADSCrossRefGoogle Scholar
  51. [51]
    K. Abe et al., Letter of Intent: The Hyper-Kamiokande ExperimentDetector Design and Physics Potential, arXiv:1109.3262 [INSPIRE].

Copyright information

© The Author(s) 2015

Authors and Affiliations

  • Keisuke Harigaya
    • 1
  • Masahiro Ibe
    • 1
    • 2
  • Motoo Suzuki
    • 1
    • 2
    Email author
  1. 1.ICRR, University of TokyoKashiwaJapan
  2. 2.Kavli IPMU (WPI), UTIASUniversity of TokyoKashiwaJapan

Personalised recommendations