Journal of High Energy Physics

, 2019:81 | Cite as

The weak scale from weak gravity

  • Nathaniel Craig
  • Isabel Garcia GarciaEmail author
  • Seth Koren
Open Access
Regular Article - Theoretical Physics


We explore the prospects for bounding the weak scale using the weak gravity conjecture (WGC), addressing the hierarchy problem by violating the expectations of effective field theory. Building on earlier work by Cheung and Remmen, we construct models in which a super-extremal particle satisfying the electric WGC for a new Abelian gauge group obtains some of its mass from the Higgs, setting an upper bound on the weak scale as other UV-insensitive parameters are held fixed. Avoiding undue sensitivity of the weak scale to the parameters entering the bound implies that the super-extremal particle must lie at or below the weak scale. While the magnetic version of the conjecture implies additional physics entering around the same scale, we demonstrate that this need not correspond to a cutoff for the Higgs potential or otherwise trivialize the bound. We stress that linking the WGC to the weak scale necessarily involves new light particles coupled to the Higgs, implying a variety of experimentally accessible signatures including invisible Higgs decays and radiative corrections in the electroweak sector. These models also give rise to natural dark matter candidates, providing additional paths to discovery. In particular, collective effects in the dark matter plasma may provide a telltale sign of the Abelian gauge group responsible for bounding the weak scale.


Beyond Standard Model Gauge Symmetry 


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.


  1. [1]
    C. Vafa, The String landscape and the swampland, hep-th/0509212 [INSPIRE].
  2. [2]
    T.D. Brennan, F. Carta and C. Vafa, The String Landscape, the Swampland and the Missing Corner, PoS(TASI2017)015 (2017) [arXiv:1711.00864] [INSPIRE].
  3. [3]
    E. Palti, The Swampland: Introduction and Review, Fortsch. Phys. 67 (2019) 1900037 [arXiv:1903.06239] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  4. [4]
    N. Arkani-Hamed, S. Dubovsky, A. Nicolis and G. Villadoro, Quantum Horizons of the Standard Model Landscape, JHEP 06 (2007) 078 [hep-th/0703067] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  5. [5]
    G. Dvali, Black Holes and Large N Species Solution to the Hierarchy Problem, Fortsch. Phys. 58 (2010) 528 [arXiv:0706.2050] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    G. Dvali and M. Redi, Black Hole Bound on the Number of Species and Quantum Gravity at LHC, Phys. Rev. D 77 (2008) 045027 [arXiv:0710.4344] [INSPIRE].
  7. [7]
    G. Dvali, M. Redi, S. Sibiryakov and A. Vainshtein, Gravity Cutoff in Theories with Large Discrete Symmetries, Phys. Rev. Lett. 101 (2008) 151603 [arXiv:0804.0769] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    C. Cheung and G.N. Remmen, Naturalness and the Weak Gravity Conjecture, Phys. Rev. Lett. 113 (2014) 051601 [arXiv:1402.2287] [INSPIRE].
  9. [9]
    H. Ooguri and C. Vafa, Non-supersymmetric AdS and the Swampland, Adv. Theor. Math. Phys. 21 (2017) 1787 [arXiv:1610.01533] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    L.E. Ibáñez, V. Martin-Lozano and I. Valenzuela, Constraining Neutrino Masses, the Cosmological Constant and BSM Physics from the Weak Gravity Conjecture, JHEP 11 (2017) 066 [arXiv:1706.05392] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  11. [11]
    L.E. Ibáñez, V. Martin-Lozano and I. Valenzuela, Constraining the EW Hierarchy from the Weak Gravity Conjecture, arXiv:1707.05811 [INSPIRE].
  12. [12]
    Y. Hamada and G. Shiu, Weak Gravity Conjecture, Multiple Point Principle and the Standard Model Landscape, JHEP 11 (2017) 043 [arXiv:1707.06326] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    D. Lüst and E. Palti, Scalar Fields, Hierarchical UV/IR Mixing and The Weak Gravity Conjecture, JHEP 02 (2018) 040 [arXiv:1709.01790] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    E. Gonzalo, A. Herráez and L.E. Ibáñez, AdS-phobia, the WGC, the Standard Model and Supersymmetry, JHEP 06 (2018) 051 [arXiv:1803.08455] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    E. Gonzalo and L.E. Ibáñez, The Fundamental Need for a SM Higgs and the Weak Gravity Conjecture, Phys. Lett. B 786 (2018) 272 [arXiv:1806.09647] [INSPIRE].
  16. [16]
    N. Craig, I. Garcia Garcia and S. Koren, Discrete Gauge Symmetries and the Weak Gravity Conjecture, JHEP 05 (2019) 140 [arXiv:1812.08181] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    N. Kaloper, Dark Energy, H 0 and Weak Gravity Conjecture, arXiv:1903.11676 [INSPIRE].
  18. [18]
    N. Arkani-Hamed, L. Motl, A. Nicolis and C. Vafa, The String landscape, black holes and gravity as the weakest force, JHEP 06 (2007) 060 [hep-th/0601001] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  19. [19]
    C. Cheung, J. Liu and G.N. Remmen, Proof of the Weak Gravity Conjecture from Black Hole Entropy, JHEP 10 (2018) 004 [arXiv:1801.08546] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    Y. Hamada, T. Noumi and G. Shiu, Weak Gravity Conjecture from Unitarity and Causality, Phys. Rev. Lett. 123 (2019) 051601 [arXiv:1810.03637] [INSPIRE].
  21. [21]
    B. Bellazzini, M. Lewandowski and J. Serra, AmplitudesPositivity, Weak Gravity Conjecture and Modified Gravity, arXiv:1902.03250 [INSPIRE].
  22. [22]
    B. Heidenreich, M. Reece and T. Rudelius, Sharpening the Weak Gravity Conjecture with Dimensional Reduction, JHEP 02 (2016) 140 [arXiv:1509.06374] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  23. [23]
    B. Heidenreich, M. Reece and T. Rudelius, Evidence for a sublattice weak gravity conjecture, JHEP 08 (2017) 025 [arXiv:1606.08437] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  24. [24]
    M. Montero, G. Shiu and P. Soler, The Weak Gravity Conjecture in three dimensions, JHEP 10 (2016) 159 [arXiv:1606.08438] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  25. [25]
    S. Andriolo, D. Junghans, T. Noumi and G. Shiu, A Tower Weak Gravity Conjecture from Infrared Consistency, Fortsch. Phys. 66 (2018) 1800020 [arXiv:1802.04287] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  26. [26]
    E. Palti, The Weak Gravity Conjecture and Scalar Fields, JHEP 08 (2017) 034 [arXiv:1705.04328] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  27. [27]
    G. ’t Hooft, Magnetic Monopoles in Unified Gauge Theories, Nucl. Phys. B 79 (1974) 276 [INSPIRE].
  28. [28]
    A.M. Polyakov, Particle Spectrum in the Quantum Field Theory, JETP Lett. 20 (1974) 194 [INSPIRE].ADSGoogle Scholar
  29. [29]
    B. Heidenreich, M. Reece and T. Rudelius, The Weak Gravity Conjecture and Emergence from an Ultraviolet Cutoff, Eur. Phys. J. C 78 (2018) 337 [arXiv:1712.01868] [INSPIRE].
  30. [30]
    P.W. Graham, D.E. Kaplan and S. Rajendran, Cosmological Relaxation of the Electroweak Scale, Phys. Rev. Lett. 115 (2015) 221801 [arXiv:1504.07551] [INSPIRE].ADSCrossRefGoogle Scholar
  31. [31]
    V. Agrawal, S.M. Barr, J.F. Donoghue and D. Seckel, Viable range of the mass scale of the standard model, Phys. Rev. D 57 (1998) 5480 [hep-ph/9707380] [INSPIRE].
  32. [32]
    D. Harlow, Wormholes, Emergent Gauge Fields and the Weak Gravity Conjecture, JHEP 01 (2016) 122 [arXiv:1510.07911] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  33. [33]
    E.G. Adelberger, J.H. Gundlach, B.R. Heckel, S. Hoedl and S. Schlamminger, Torsion balance experiments: A low-energy frontier of particle physics, Prog. Part. Nucl. Phys. 62 (2009) 102 [INSPIRE].ADSCrossRefGoogle Scholar
  34. [34]
    T.A. Wagner, S. Schlamminger, J.H. Gundlach and E.G. Adelberger, Torsion-balance tests of the weak equivalence principle, Class. Quant. Grav. 29 (2012) 184002 [arXiv:1207.2442] [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    R. Slansky, Group Theory for Unified Model Building, Phys. Rept. 79 (1981) 1 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  36. [36]
    P. Saraswat, Weak gravity conjecture and effective field theory, Phys. Rev. D 95 (2017) 025013 [arXiv:1608.06951] [INSPIRE].
  37. [37]
    R. Barbieri and G.F. Giudice, Upper Bounds on Supersymmetric Particle Masses, Nucl. Phys. B 306 (1988) 63 [INSPIRE].
  38. [38]
    R. Contino, D. Greco, R. Mahbubani, R. Rattazzi and R. Torre, Precision Tests and Fine Tuning in Twin Higgs Models, Phys. Rev. D 96 (2017) 095036 [arXiv:1702.00797] [INSPIRE].
  39. [39]
    X.-G. Wen and E. Witten, Electric and Magnetic Charges in Superstring Models, Nucl. Phys. B 261 (1985) 651 [INSPIRE].
  40. [40]
    R.d. Sorkin, Kaluza-Klein Monopole, Phys. Rev. Lett. 51 (1983) 87 [INSPIRE].
  41. [41]
    D.J. Gross and M.J. Perry, Magnetic Monopoles in Kaluza-Klein Theories, Nucl. Phys. B 226 (1983) 29 [INSPIRE].
  42. [42]
    N. Arkani-Hamed, S. Dimopoulos and G.R. Dvali, The Hierarchy problem and new dimensions at a millimeter, Phys. Lett. B 429 (1998) 263 [hep-ph/9803315] [INSPIRE].
  43. [43]
    T. Han, J.D. Lykken and R.-J. Zhang, On Kaluza-Klein states from large extra dimensions, Phys. Rev. D 59 (1999) 105006 [hep-ph/9811350] [INSPIRE].
  44. [44]
    M. Reece, Photon Masses in the Landscape and the Swampland, JHEP 07 (2019) 181 [arXiv:1808.09966] [INSPIRE].ADSCrossRefGoogle Scholar
  45. [45]
    A. Crivellin, G. D’Ambrosio and J. Heeck, Addressing the LHC flavor anomalies with horizontal gauge symmetries, Phys. Rev. D 91 (2015) 075006 [arXiv:1503.03477] [INSPIRE].
  46. [46]
    R. Foot, New Physics From Electric Charge Quantization?, Mod. Phys. Lett. A 6 (1991) 527 [INSPIRE].
  47. [47]
    X.G. He, G.C. Joshi, H. Lew and R.R. Volkas, New-Z phenomenology, Phys. Rev. D 43 (1991) 22 [INSPIRE].
  48. [48]
    V. Silveira and A. Zee, Scalar phantoms, Phys. Lett. 161B (1985) 136 [INSPIRE].
  49. [49]
    J. McDonald, Gauge singlet scalars as cold dark matter, Phys. Rev. D 50 (1994) 3637 [hep-ph/0702143] [INSPIRE].
  50. [50]
    C.P. Burgess, M. Pospelov and T. ter Veldhuis, The Minimal model of nonbaryonic dark matter: A Singlet scalar, Nucl. Phys. B 619 (2001) 709 [hep-ph/0011335] [INSPIRE].
  51. [51]
    CMS collaboration, Searches for invisible decays of the Higgs boson in pp collisions at \( \sqrt{s} \) = 7,8 and 13 TeV, JHEP 02 (2017) 135 [arXiv:1610.09218] [INSPIRE].
  52. [52]
    ATLAS collaboration, Constraints on new phenomena via Higgs boson couplings and invisible decays with the ATLAS detector, JHEP 11 (2015) 206 [arXiv:1509.00672] [INSPIRE].
  53. [53]
    ATLAS collaboration, Search for an invisibly decaying Higgs boson or dark matter candidates produced in association with a Z boson in pp collisions at \( \sqrt{s} \) = 13 TeV with the ATLAS detector, Phys. Lett. B 776 (2018) 318 [arXiv:1708.09624] [INSPIRE].
  54. [54]
    ATLAS collaboration, Search for invisible decays of a Higgs boson using vector-boson fusion in pp collisions at \( \sqrt{s} \) = 8 TeV with the ATLAS detector, JHEP 01 (2016) 172 [arXiv:1508.07869] [INSPIRE].
  55. [55]
    CMS collaboration, Search for invisible decays of a Higgs boson produced through vector boson fusion in proton-proton collisions at \( \sqrt{s} \) = 13 TeV, Phys. Lett. B 793 (2019) 520 [arXiv:1809.05937] [INSPIRE].
  56. [56]
    ATLAS collaboration, Search for invisible Higgs boson decays in vector boson fusion at \( \sqrt{s} \) = 13 TeV with the ATLAS detector, Phys. Lett. B 793 (2019) 499 [arXiv:1809.06682] [INSPIRE].
  57. [57]
    CMS collaboration, Projected performance of Higgs analyses at the HL-LHC for ECFA 2016, CMS-PAS-FTR-16-002.
  58. [58]
    N. Craig, H.K. Lou, M. McCullough and A. Thalapillil, The Higgs Portal Above Threshold, JHEP 02 (2016) 127 [arXiv:1412.0258] [INSPIRE].ADSCrossRefGoogle Scholar
  59. [59]
    C. Englert and M. McCullough, Modified Higgs Sectors and NLO Associated Production, JHEP 07 (2013) 168 [arXiv:1303.1526] [INSPIRE].ADSCrossRefGoogle Scholar
  60. [60]
    N. Craig, C. Englert and M. McCullough, New Probe of Naturalness, Phys. Rev. Lett. 111 (2013) 121803 [arXiv:1305.5251] [INSPIRE].ADSCrossRefGoogle Scholar
  61. [61]
    A. Freitas, S. Westhoff and J. Zupan, Integrating in the Higgs Portal to Fermion Dark Matter, JHEP 09 (2015) 015 [arXiv:1506.04149] [INSPIRE].CrossRefGoogle Scholar
  62. [62]
    M.A. Fedderke, T. Lin and L.-T. Wang, Probing the fermionic Higgs portal at lepton colliders, JHEP 04 (2016) 160 [arXiv:1506.05465] [INSPIRE].ADSGoogle Scholar
  63. [63]
    C.E. Yaguna, Singlet-Doublet Dirac Dark Matter, Phys. Rev. D 92 (2015) 115002 [arXiv:1510.06151] [INSPIRE].
  64. [64]
    XENON collaboration, Dark Matter Search Results from a One Ton-Year Exposure of XENON1T, Phys. Rev. Lett. 121 (2018) 111302 [arXiv:1805.12562] [INSPIRE].
  65. [65]
    G. Arcadi, A. Djouadi and M. Raidal, Dark Matter through the Higgs portal, arXiv:1903.03616 [INSPIRE].
  66. [66]
    L.J. Hall, K. Jedamzik, J. March-Russell and S.M. West, Freeze-In Production of FIMP Dark Matter, JHEP 03 (2010) 080 [arXiv:0911.1120] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  67. [67]
    C.E. Yaguna, The Singlet Scalar as FIMP Dark Matter, JHEP 08 (2011) 060 [arXiv:1105.1654] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  68. [68]
    M. Frigerio, T. Hambye and E. Masso, Sub-GeV dark matter as pseudo-Goldstone from the seesaw scale, Phys. Rev. X 1 (2011) 021026 [arXiv:1107.4564] [INSPIRE].
  69. [69]
    X. Chu, T. Hambye and M.H.G. Tytgat, The Four Basic Ways of Creating Dark Matter Through a Portal, JCAP 05 (2012) 034 [arXiv:1112.0493] [INSPIRE].ADSCrossRefGoogle Scholar
  70. [70]
    L. Ackerman, M.R. Buckley, S.M. Carroll and M. Kamionkowski, Dark Matter and Dark Radiation, Phys. Rev. D 79 (2009) 023519 [arXiv:0810.5126] [INSPIRE].
  71. [71]
    J. Mardon, A (Nearly) Weaker-Than-Gravity Bound on Dark Matter Electromagnetism, talk at Perimeter Institute, 10 May 2016 [].
  72. [72]
    M. Heikinheimo, M. Raidal, C. Spethmann and H. Veermäe, Dark matter self-interactions via collisionless shocks in cluster mergers, Phys. Lett. B 749 (2015) 236 [arXiv:1504.04371] [INSPIRE].
  73. [73]
    M. Heikinheimo, M. Raidal, C. Spethmann and H. Veermae, Collisionless shocks in self-interacting dark matter, Plasma Phys. Control. Fusion 60 (2017) 014011 [arXiv:1707.03662] [INSPIRE].
  74. [74]
    C. Spethmann et al., Simulations of Galaxy Cluster Collisions with a Dark Plasma Component, Astron. Astrophys. 608 (2017) A125 [arXiv:1603.07324] [INSPIRE].CrossRefGoogle Scholar
  75. [75]
    A. Mahdavi, H.y. Hoekstra, A.y. Babul, D.y. Balam and P. Capak, A Dark Core in Abell 520, Astrophys. J. 668 (2007) 806 [arXiv:0706.3048] [INSPIRE].
  76. [76]
    M.J. Jee, H. Hoekstra, A. Mahdavi and A. Babul, Hubble Space Telescope/Advanced Camera for Surveys Confirmation of the Dark Substructure in A520, Astrophys. J. 783 (2014) 78 [arXiv:1401.3356] [INSPIRE].ADSCrossRefGoogle Scholar
  77. [77]
    A. Bret, Weibel, Two-Stream, Filamentation, Oblique, Bell, Buneman. . . which one grows faster?, Astrophys. J. 699 (2009) 990 [arXiv:0903.2658] [INSPIRE].
  78. [78]
    M.E. Dieckmann and A. Bret, Simulation study of the formation of a non-relativistic pair shock, J. Plasma Phys. 83 (2017) 019004 [arXiv:1701.04075] [INSPIRE].
  79. [79]
    M.E. Dieckmann and A. Bret, Electrostatic and magnetic instabilities in the transition layer of a collisionless weakly relativistic pair shock, Mon. Not. Roy. Astron. Soc. 473 (2018) 198 [arXiv:1709.02961] [INSPIRE].ADSCrossRefGoogle Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  • Nathaniel Craig
    • 1
  • Isabel Garcia Garcia
    • 2
    Email author
  • Seth Koren
    • 1
  1. 1.Department of PhysicsUniversity of CaliforniaSanta BarbaraU.S.A.
  2. 2.Kavli Institute for Theoretical PhysicsUniversity of CaliforniaSanta BarbaraU.S.A.

Personalised recommendations