Journal of High Energy Physics

, 2016:16 | Cite as

Implications of unitarity and gauge invariance for simplified dark matter models

  • Felix Kahlhoefer
  • Kai Schmidt-Hoberg
  • Thomas Schwetz
  • Stefan Vogl
Open Access
Regular Article - Theoretical Physics

Abstract

We show that simplified models used to describe the interactions of dark matter with Standard Model particles do not in general respect gauge invariance and that perturbative unitarity may be violated in large regions of the parameter space. The modifications necessary to cure these inconsistencies may imply a much richer phenomenology and lead to stringent constraints on the model. We illustrate these observations by considering the simplified model of a fermionic dark matter particle and a vector mediator. Imposing gauge invariance then leads to strong constraints from dilepton resonance searches and electroweak precision tests. Furthermore, the new states required to restore perturbative unitarity can mix with Standard Model states and mediate interactions between the dark and the visible sector, leading to new experimental signatures such as invisible Higgs decays. The resulting constraints are typically stronger than the ‘classic’ constraints on DM simplified models such as monojet searches and make it difficult to avoid thermal overproduction of dark matter.

Keywords

Beyond Standard Model Cosmology of Theories beyond the SM 

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]
    M. Beltrán, D. Hooper, E.W. Kolb and Z.C. Krusberg, Deducing the nature of dark matter from direct and indirect detection experiments in the absence of collider signatures of new physics, Phys. Rev. D 80 (2009) 043509 [arXiv:0808.3384] [INSPIRE].ADSGoogle Scholar
  2. [2]
    M. Beltrán, D. Hooper, E.W. Kolb, Z.A.C. Krusberg and T.M.P. Tait, Maverick dark matter at colliders, JHEP 09 (2010) 037 [arXiv:1002.4137] [INSPIRE].CrossRefADSGoogle Scholar
  3. [3]
    J. Goodman, M. Ibe, A. Rajaraman, W. Shepherd, T.M.P. Tait and H.-B. Yu, Constraints on Dark Matter from Colliders, Phys. Rev. D 82 (2010) 116010 [arXiv:1008.1783] [INSPIRE].ADSGoogle Scholar
  4. [4]
    P.J. Fox, R. Harnik, J. Kopp and Y. Tsai, Missing Energy Signatures of Dark Matter at the LHC, Phys. Rev. D 85 (2012) 056011 [arXiv:1109.4398] [INSPIRE].ADSGoogle Scholar
  5. [5]
    A. Rajaraman, W. Shepherd, T.M.P. Tait and A.M. Wijangco, LHC Bounds on Interactions of Dark Matter, Phys. Rev. D 84 (2011) 095013 [arXiv:1108.1196] [INSPIRE].ADSGoogle Scholar
  6. [6]
    I.M. Shoemaker and L. Vecchi, Unitarity and Monojet Bounds on Models for DAMA, CoGeNT and CRESST-II, Phys. Rev. D 86 (2012) 015023 [arXiv:1112.5457] [INSPIRE].ADSGoogle Scholar
  7. [7]
    P.J. Fox, R. Harnik, R. Primulando and C.-T. Yu, Taking a Razor to Dark Matter Parameter Space at the LHC, Phys. Rev. D 86 (2012) 015010 [arXiv:1203.1662] [INSPIRE].ADSGoogle Scholar
  8. [8]
    G. Busoni, A. De Simone, E. Morgante and A. Riotto, On the Validity of the Effective Field Theory for Dark Matter Searches at the LHC, Phys. Lett. B 728 (2014) 412 [arXiv:1307.2253] [INSPIRE].CrossRefADSGoogle Scholar
  9. [9]
    G. Busoni, A. De Simone, J. Gramling, E. Morgante and A. Riotto, On the Validity of the Effective Field Theory for Dark Matter Searches at the LHC, Part II: Complete Analysis for the s-channel, JCAP 06 (2014) 060 [arXiv:1402.1275] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  10. [10]
    Q.-F. Xiang, X.-J. Bi, P.-F. Yin and Z.-H. Yu, Searches for dark matter signals in simplified models at future hadron colliders, Phys. Rev. D 91 (2015) 095020 [arXiv:1503.02931] [INSPIRE].ADSGoogle Scholar
  11. [11]
    K. Griest and M. Kamionkowski, Unitarity Limits on the Mass and Radius of Dark Matter Particles, Phys. Rev. Lett. 64 (1990) 615 [INSPIRE].CrossRefADSGoogle Scholar
  12. [12]
    D.G.E. Walker, Unitarity Constraints on Higgs Portals, arXiv:1310.1083 [INSPIRE].
  13. [13]
    M. Endo and Y. Yamamoto, Unitarity Bounds on Dark Matter Effective Interactions at LHC, JHEP 06 (2014) 126 [arXiv:1403.6610] [INSPIRE].CrossRefADSGoogle Scholar
  14. [14]
    S. El Hedri, W. Shepherd and D.G.E. Walker, Perturbative Unitarity Constraints on Gauge Portals, arXiv:1412.5660 [INSPIRE].
  15. [15]
    J. Abdallah et al., Simplified Models for Dark Matter Searches at the LHC, Phys. Dark Univ. 9-10 (2015) 8 [arXiv:1506.03116] [INSPIRE].CrossRefGoogle Scholar
  16. [16]
    O. Buchmueller, M.J. Dolan and C. McCabe, Beyond Effective Field Theory for Dark Matter Searches at the LHC, JHEP 01 (2014) 025 [arXiv:1308.6799] [INSPIRE].CrossRefADSGoogle Scholar
  17. [17]
    O. Buchmueller, M.J. Dolan, S.A. Malik and C. McCabe, Characterising dark matter searches at colliders and direct detection experiments: Vector mediators, JHEP 01 (2015) 037 [arXiv:1407.8257] [INSPIRE].CrossRefADSGoogle Scholar
  18. [18]
    P. Harris, V.V. Khoze, M. Spannowsky and C. Williams, Constraining Dark Sectors at Colliders: Beyond the Effective Theory Approach, Phys. Rev. D 91 (2015) 055009 [arXiv:1411.0535] [INSPIRE].ADSGoogle Scholar
  19. [19]
    M. Garny, A. Ibarra, S. Rydbeck and S. Vogl, Majorana Dark Matter with a Coloured Mediator: Collider vs Direct and Indirect Searches, JHEP 06 (2014) 169 [arXiv:1403.4634] [INSPIRE].CrossRefADSGoogle Scholar
  20. [20]
    M.R. Buckley, D. Feld and D. Goncalves, Scalar Simplified Models for Dark Matter, Phys. Rev. D 91 (2015) 015017 [arXiv:1410.6497] [INSPIRE].ADSGoogle Scholar
  21. [21]
    T. Jacques and K. Nordström, Mapping monojet constraints onto Simplified Dark Matter Models, JHEP 06 (2015) 142 [arXiv:1502.05721] [INSPIRE].CrossRefADSGoogle Scholar
  22. [22]
    A. Alves and K. Sinha, Searches for Dark Matter at the LHC: A Multivariate Analysis in the Mono-Z Channel, Phys. Rev. D 92 (2015) 115013 [arXiv:1507.08294] [INSPIRE].ADSGoogle Scholar
  23. [23]
    A. Choudhury, K. Kowalska, L. Roszkowski, E.M. Sessolo and A.J. Williams, Less-simplified models of dark matter for direct detection and the LHC, arXiv:1509.05771 [INSPIRE].
  24. [24]
    M.T. Frandsen, F. Kahlhoefer, A. Preston, S. Sarkar and K. Schmidt-Hoberg, LHC and Tevatron Bounds on the Dark Matter Direct Detection Cross-Section for Vector Mediators, JHEP 07 (2012) 123 [arXiv:1204.3839] [INSPIRE].CrossRefADSGoogle Scholar
  25. [25]
    M. Fairbairn and J. Heal, Complementarity of dark matter searches at resonance, Phys. Rev. D 90 (2014) 115019 [arXiv:1406.3288] [INSPIRE].ADSGoogle Scholar
  26. [26]
    M. Chala, F. Kahlhoefer, M. McCullough, G. Nardini and K. Schmidt-Hoberg, Constraining Dark Sectors with Monojets and Dijets, JHEP 07 (2015) 089 [arXiv:1503.05916] [INSPIRE].CrossRefADSGoogle Scholar
  27. [27]
    G. Busoni, A. De Simone, T. Jacques, E. Morgante and A. Riotto, Making the Most of the Relic Density for Dark Matter Searches at the LHC 14 TeV Run, JCAP 03 (2015) 022 [arXiv:1410.7409] [INSPIRE].CrossRefADSGoogle Scholar
  28. [28]
    M. Blennow, J. Herrero-Garcia, T. Schwetz and S. Vogl, Halo-independent tests of dark matter direct detection signals: local DM density, LHC and thermal freeze-out, JCAP 08 (2015) 039 [arXiv:1505.05710] [INSPIRE].CrossRefADSGoogle Scholar
  29. [29]
    CMS collaboration, Search for dark matter, extra dimensions and unparticles in monojet events in proton-proton collisions at \( \sqrt{s}=8 \) TeV, Eur. Phys. J. C 75 (2015) 235 [arXiv:1408.3583] [INSPIRE].
  30. [30]
    ATLAS collaboration, Search for new phenomena in final states with an energetic jet and large missing transverse momentum in pp collisions at \( \sqrt{s}=8 \) TeV with the ATLAS detector, Eur. Phys. J. C 75 (2015) 299 [arXiv:1502.01518] [INSPIRE].
  31. [31]
    D. Abercrombie et al., Dark Matter Benchmark Models for Early LHC Run-2 Searches: Report of the ATLAS/CMS Dark Matter Forum, arXiv:1507.00966 [INSPIRE].
  32. [32]
    E. Dudas, Y. Mambrini, S. Pokorski and A. Romagnoni, (In)visible Z-prime and dark matter, JHEP 08 (2009) 014 [arXiv:0904.1745] [INSPIRE].
  33. [33]
    P.J. Fox, J. Liu, D. Tucker-Smith and N. Weiner, An Effective Z’, Phys. Rev. D 84 (2011) 115006 [arXiv:1104.4127] [INSPIRE].ADSGoogle Scholar
  34. [34]
    A. Alves, S. Profumo and F.S. Queiroz, The dark Z portal: direct, indirect and collider searches, JHEP 04 (2014) 063 [arXiv:1312.5281] [INSPIRE].CrossRefADSGoogle Scholar
  35. [35]
    G. Arcadi, Y. Mambrini, M.H.G. Tytgat and B. Zaldivar, Invisible Z and dark matter: LHC vs LUX constraints, JHEP 03 (2014) 134 [arXiv:1401.0221] [INSPIRE].CrossRefADSGoogle Scholar
  36. [36]
    C.B. Jackson, G. Servant, G. Shaughnessy, T.M.P. Tait and M. Taoso, Gamma-ray lines and One-Loop Continuum from s-channel Dark Matter Annihilations, JCAP 07 (2013) 021 [arXiv:1302.1802] [INSPIRE].CrossRefADSGoogle Scholar
  37. [37]
    C.B. Jackson, G. Servant, G. Shaughnessy, T.M.P. Tait and M. Taoso, Gamma Rays from Top-Mediated Dark Matter Annihilations, JCAP 07 (2013) 006 [arXiv:1303.4717] [INSPIRE].CrossRefADSGoogle Scholar
  38. [38]
    M. Duerr and P. Fileviez Perez, Baryonic Dark Matter, Phys. Lett. B 732 (2014) 101 [arXiv:1309.3970] [INSPIRE].CrossRefADSGoogle Scholar
  39. [39]
    M. Duerr and P. Fileviez Perez, Theory for Baryon Number and Dark Matter at the LHC, Phys. Rev. D 91 (2015) 095001 [arXiv:1409.8165] [INSPIRE].ADSGoogle Scholar
  40. [40]
    O. Lebedev and Y. Mambrini, Axial dark matter: The case for an invisible Z , Phys. Lett. B 734 (2014) 350 [arXiv:1403.4837] [INSPIRE].CrossRefADSGoogle Scholar
  41. [41]
    D. Hooper, Z mediated dark matter models for the Galactic Center gamma-ray excess, Phys. Rev. D 91 (2015) 035025 [arXiv:1411.4079] [INSPIRE].ADSGoogle Scholar
  42. [42]
    V.M. Lozano, M. Peiró and P. Soler, Isospin violating dark matter in Stückelberg portal scenarios, JHEP 04 (2015) 175 [arXiv:1503.01780] [INSPIRE].CrossRefADSGoogle Scholar
  43. [43]
    A. Alves, A. Berlin, S. Profumo and F.S. Queiroz, Dark Matter Complementarity and the Z Portal, Phys. Rev. D 92 (2015) 083004 [arXiv:1501.03490] [INSPIRE].ADSGoogle Scholar
  44. [44]
    A. Alves, A. Berlin, S. Profumo and F.S. Queiroz, Dirac-fermionic dark matter in U(1)X models, JHEP 10 (2015) 076 [arXiv:1506.06767] [INSPIRE].CrossRefADSGoogle Scholar
  45. [45]
    M. Duerr, P. Fileviez Perez and J. Smirnov, Simplified Dirac Dark Matter Models and Gamma-Ray Lines, Phys. Rev. D 92 (2015) 083521 [arXiv:1506.05107] [INSPIRE].ADSGoogle Scholar
  46. [46]
    J. Heisig, M. Krämer, M. Pellen and C. Wiebusch, Constraints on Majorana Dark Matter from the LHC and IceCube, arXiv:1509.07867 [INSPIRE].
  47. [47]
    B. Holdom, Two U(1)’s and Epsilon Charge Shifts, Phys. Lett. B 166 (1986) 196 [INSPIRE].CrossRefADSGoogle Scholar
  48. [48]
    K.S. Babu, C.F. Kolda and J. March-Russell, Implications of generalized ZZ mixing, Phys. Rev. D 57 (1998) 6788 [hep-ph/9710441] [INSPIRE].
  49. [49]
    B.W. Lee, C. Quigg and H.B. Thacker, Weak Interactions at Very High-Energies: The Role of the Higgs Boson Mass, Phys. Rev. D 16 (1977) 1519 [INSPIRE].ADSGoogle Scholar
  50. [50]
    N.F. Bell, Y. Cai, J.B. Dent, R.K. Leane and T.J. Weiler, Dark matter at the LHC: Effective field theories and gauge invariance, Phys. Rev. D 92 (2015) 053008 [arXiv:1503.07874] [INSPIRE].ADSGoogle Scholar
  51. [51]
    M.S. Chanowitz, M.A. Furman and I. Hinchliffe, Weak Interactions of Ultraheavy Fermions. 2., Nucl. Phys. B 153 (1979) 402 [INSPIRE].
  52. [52]
    A. Schuessler and D. Zeppenfeld, Unitarity constraints on MSSM trilinear couplings, in proceedings of The 15th International Conference on Supersymmetry and Unification of Fundamental Interactions (SUSY 2007), July 26 - August 1, 2007, Karlsruhe, Germany, http://www.susy07.uni-karlsruhe.de/Proceedings/proceedings/susy07.pdf [arXiv:0710.5175] [INSPIRE].
  53. [53]
    J. Shu, Unitarity Bounds for New Physics from Axial Coupling at LHC, Phys. Rev. D 78 (2008) 096004 [arXiv:0711.2516] [INSPIRE].ADSGoogle Scholar
  54. [54]
    M. Hosch, K. Whisnant and B.-L. Young, Unitarity constraints on anomalous top quark couplings to weak gauge bosons, Phys. Rev. D 55 (1997) 3137 [hep-ph/9607413] [INSPIRE].
  55. [55]
    K.S. Babu, J. Julio and Y. Zhang, Perturbative unitarity constraints on general W’ models and collider implications, Nucl. Phys. B 858 (2012) 468 [arXiv:1111.5021] [INSPIRE].CrossRefADSMATHGoogle Scholar
  56. [56]
    E.C.G. Stueckelberg, Interaction energy in electrodynamics and in the field theory of nuclear forces, Helv. Phys. Acta 11 (1938) 225 [INSPIRE].Google Scholar
  57. [57]
    B. Körs and P. Nath, Aspects of the Stueckelberg extension, JHEP 07 (2005) 069 [hep-ph/0503208] [INSPIRE].
  58. [58]
    LUX collaboration, D.S. Akerib et al., First results from the LUX dark matter experiment at the Sanford Underground Research Facility, Phys. Rev. Lett. 112 (2014) 091303 [arXiv:1310.8214] [INSPIRE].
  59. [59]
    L. Lopez-Honorez, T. Schwetz and J. Zupan, Higgs portal, fermionic dark matter and a Standard Model like Higgs at 125 GeV, Phys. Lett. B 716 (2012) 179 [arXiv:1203.2064] [INSPIRE].CrossRefADSGoogle Scholar
  60. [60]
    L. Basso, S. Moretti and G.M. Pruna, Theoretical constraints on the couplings of non-exotic minimal Z bosons, JHEP 08 (2011) 122 [arXiv:1106.4762] [INSPIRE].CrossRefADSMATHGoogle Scholar
  61. [61]
    M. Carena, A. Daleo, B.A. Dobrescu and T.M.P. Tait, Z gauge bosons at the Tevatron, Phys. Rev. D 70 (2004) 093009 [hep-ph/0408098] [INSPIRE].
  62. [62]
    Particle Data Group collaboration, K.A. Olive et al., Review of Particle Physics, Chin. Phys. C 38 (2014) 090001 [INSPIRE].
  63. [63]
    T. Appelquist, B.A. Dobrescu and A.R. Hopper, Nonexotic neutral gauge bosons, Phys. Rev. D 68 (2003) 035012 [hep-ph/0212073] [INSPIRE].
  64. [64]
    SLD Electroweak Group, SLD Heavy Flavor Group, LEP Electroweak Working Group, DELPHI, LEP, ALEPH, OPAL, L3 collaborations, A combination of preliminary electroweak measurements and constraints on the standard model, hep-ex/0312023 [INSPIRE].
  65. [65]
    ATLAS collaboration, Search for high-mass dilepton resonances in pp collisions at \( \sqrt{s}=8 \) TeV with the ATLAS detector, Phys. Rev. D 90 (2014) 052005 [arXiv:1405.4123] [INSPIRE].
  66. [66]
    CDF, D0 collaborations, M. Jaffre, Search for high mass resonances in dilepton, dijet and diboson final states at the Tevatron, PoS(EPS-HEP 2009)244 [arXiv:0909.2979] [INSPIRE].
  67. [67]
    M.T. Frandsen, F. Kahlhoefer, S. Sarkar and K. Schmidt-Hoberg, Direct detection of dark matter in models with a light Z’, JHEP 09 (2011) 128 [arXiv:1107.2118] [INSPIRE].CrossRefADSGoogle Scholar
  68. [68]
    B. Feldstein and F. Kahlhoefer, Quantifying (dis)agreement between direct detection experiments in a halo-independent way, JCAP 12 (2014) 052 [arXiv:1409.5446] [INSPIRE].CrossRefADSGoogle Scholar
  69. [69]
    G. Bélanger, F. Boudjema, A. Pukhov and A. Semenov, MicrOMEGAs4.1: two dark matter candidates, Comput. Phys. Commun. 192 (2015) 322 [arXiv:1407.6129] [INSPIRE].CrossRefADSGoogle Scholar
  70. [70]
    A. Alloul, N.D. Christensen, C. Degrande, C. Duhr and B. Fuks, FeynRules 2.0 - A complete toolbox for tree-level phenomenology, Comput. Phys. Commun. 185 (2014) 2250 [arXiv:1310.1921] [INSPIRE].
  71. [71]
    J. Alwall et al., The automated computation of tree-level and next-to-leading order differential cross sections and their matching to parton shower simulations, JHEP 07 (2014) 079 [arXiv:1405.0301] [INSPIRE].CrossRefADSGoogle Scholar
  72. [72]
    T. Sjöstrand, S. Mrenna and P.Z. Skands, PYTHIA 6.4 Physics and Manual, JHEP 05 (2006) 026 [hep-ph/0603175] [INSPIRE].
  73. [73]
    A. Belyaev, N.D. Christensen and A. Pukhov, CalcHEP 3.4 for collider physics within and beyond the Standard Model, Comput. Phys. Commun. 184 (2013) 1729 [arXiv:1207.6082] [INSPIRE].
  74. [74]
    DELPHES 3 collaboration, J. de Favereau et al., DELPHES 3, A modular framework for fast simulation of a generic collider experiment, JHEP 02 (2014) 057 [arXiv:1307.6346] [INSPIRE].
  75. [75]
    C.D. Carone and H. Murayama, Realistic models with a light U(1) gauge boson coupled to baryon number, Phys. Rev. D 52 (1995) 484 [hep-ph/9501220] [INSPIRE].
  76. [76]
    U. Haisch and F. Kahlhoefer, On the importance of loop-induced spin-independent interactions for dark matter direct detection, JCAP 04 (2013) 050 [arXiv:1302.4454] [INSPIRE].CrossRefADSGoogle Scholar
  77. [77]
    A. Djouadi, O. Lebedev, Y. Mambrini and J. Quevillon, Implications of LHC searches for Higgs-portal dark matter, Phys. Lett. B 709 (2012) 65 [arXiv:1112.3299] [INSPIRE].CrossRefADSGoogle Scholar
  78. [78]
    O. Lebedev, On Stability of the Electroweak Vacuum and the Higgs Portal, Eur. Phys. J. C 72 (2012) 2058 [arXiv:1203.0156] [INSPIRE].CrossRefADSGoogle Scholar
  79. [79]
    S. Baek, P. Ko, W.-I. Park and E. Senaha, Vacuum structure and stability of a singlet fermion dark matter model with a singlet scalar messenger, JHEP 11 (2012) 116 [arXiv:1209.4163] [INSPIRE].CrossRefADSGoogle Scholar
  80. [80]
    S. Esch, M. Klasen and C.E. Yaguna, Detection prospects of singlet fermionic dark matter, Phys. Rev. D 88 (2013) 075017 [arXiv:1308.0951] [INSPIRE].ADSGoogle Scholar
  81. [81]
    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
  82. [82]
    CMS collaboration, Precise determination of the mass of the Higgs boson and tests of compatibility of its couplings with the standard model predictions using proton collisions at 7 and 8 TeV, Eur. Phys. J. C 75 (2015) 212 [arXiv:1412.8662] [INSPIRE].
  83. [83]
    ATLAS, CMS collaborations, Measurements of the Higgs boson production and decay rates and constraints on its couplings from a combined ATLAS and CMS analysis of the LHC pp collision data at \( \sqrt{s}=7 \) and 8 TeV, ATLAS-CONF-2015-044 (2015).
  84. [84]
    M. Duerr, F. Kahlhoefer, K. Schmidt-Hoberg, T. Schwetz and S. Vogl, in preparation (2016).Google Scholar
  85. [85]
    E.J. Chun, J.-C. Park and S. Scopel, Dark matter and a new gauge boson through kinetic mixing, JHEP 02 (2011) 100 [arXiv:1011.3300] [INSPIRE].CrossRefADSMATHGoogle Scholar

Copyright information

© The Author(s) 2016

Authors and Affiliations

  • Felix Kahlhoefer
    • 1
  • Kai Schmidt-Hoberg
    • 1
  • Thomas Schwetz
    • 2
  • Stefan Vogl
    • 2
    • 3
  1. 1.DESYHamburgGermany
  2. 2.Institut für Kernphysik, Karlsruher Institut für Technologie (KIT)KarlsruheGermany
  3. 3.Oskar Klein Centre for Cosmoparticle Physics, Department of PhysicsStockholm UniversityStockholmSweden

Personalised recommendations