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Beyond effective field theory for dark matter searches at the LHC


We study the validity of effective field theory (EFT) interpretations of monojet searches for dark matter at the LHC for vector and axial-vector interactions. We show that the EFT approach is valid when the mediator has mass m med greater than 2.5 TeV. We find that the current limits on the contact interaction scale Λ in the EFT apply to theories that are perturbative for dark matter mass m DM< 800 GeV. However, for all values of m DM in these theories, the mediator width is larger than the mass, so that a particle-like interpretation of the mediator is doubtful. Furthermore, consistency with the thermal relic density occurs only for 170 ≲ m DM ≲ 510 GeV. For lighter mediator masses, the EFT limit either under-estimates the true limit (because the process is resonantly enhanced) or over-estimates it (because the missing energy distribution is too soft). We give some ‘rules of thumb’ that can be used to estimate the limit on Λ (to an accuracy of ~ 50 %) for any m DM and m med from knowledge of the EFT limit. We also compare the relative sensitivities of monojet and dark matter direct detection searches finding that both dominate in different regions of the m DM - m med plane. Comparing only the EFT limit with direct searches is misleading and can lead to incorrect conclusions about the relative sensitivity of the two search approaches.


  1. [1]

    Q.-H. Cao, C.-R. Chen, C.S. Li and H. Zhang, Effective dark matter model: relic density, CDMS II, Fermi LAT and LHC, JHEP 08 (2011) 018 [arXiv:0912.4511] [INSPIRE].

    Google Scholar 

  2. [2]

    M. Beltrán, D. Hooper, E.W. Kolb, Z.A. Krusberg and T.M. Tait, Maverick dark matter at colliders, JHEP 09 (2010) 037 [arXiv:1002.4137] [INSPIRE].

    ADS  Article  Google Scholar 

  3. [3]

    J. Goodman et al., Constraints on light Majorana dark matter from colliders, Phys. Lett. B 695 (2011) 185 [arXiv:1005.1286] [INSPIRE].

    ADS  Article  Google Scholar 

  4. [4]

    Y. Bai, P.J. Fox and R. Harnik, The Tevatron at the frontier of dark matter direct detection, JHEP 12 (2010) 048 [arXiv:1005.3797] [INSPIRE].

    ADS  Article  Google Scholar 

  5. [5]

    J. Goodman et al., Constraints on dark matter from colliders, Phys. Rev. D 82 (2010) 116010 [arXiv:1008.1783] [INSPIRE].

    ADS  Google Scholar 

  6. [6]

    P.J. Fox, R. Harnik, J. Kopp and Y. Tsai, LEP shines light on dark matter, Phys. Rev. D 84 (2011) 014028 [arXiv:1103.0240] [INSPIRE].

    ADS  Google Scholar 

  7. [7]

    A. Rajaraman, W. Shepherd, T.M. Tait and A.M. Wijangco, LHC bounds on interactions of dark matter, Phys. Rev. D 84 (2011) 095013 [arXiv:1108.1196] [INSPIRE].

    ADS  Google Scholar 

  8. [8]

    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].

    ADS  Google Scholar 

  9. [9]

    A. Nelson, L.M. Carpenter, R. Cotta, A. Johnstone and D. Whiteson, Confronting the Fermi line with LHC data: an effective theory of dark matter interaction with photons, arXiv:1307.5064 [INSPIRE].

  10. [10]

    ATLAS collaboration, Search for dark matter candidates and large extra dimensions in events with a jet and missing transverse momentum with the ATLAS detector, JHEP 04 (2013) 075 [arXiv:1210.4491] [INSPIRE].

    ADS  Google Scholar 

  11. [11]

    ATLAS collaboration, Search for new phenomena in monojet plus missing transverse momentum final states using 10 fb−1 of pp collisions at \( \sqrt{s} \) = 8 TeV with the ATLAS detector at the LHC, ATLAS-CONF-2012-147, CERN, Geneva Switzerland (2012).

  12. [12]

    CMS collaboration, Search for dark matter and large extra dimensions in monojet events in pp collisions at \( \sqrt{s} \) = 7 TeV, JHEP 09 (2012) 094 [arXiv:1206.5663] [INSPIRE].

    ADS  Google Scholar 

  13. [13]

    CMS collaboration, Search for new physics in monojet events in pp collisions at \( \sqrt{s} \) = 8 TeV, CMS-PAS-EXO-12-048, CERN, Geneva Switzerland (2012).

  14. [14]

    LHC New Physics Working Group collaboration, D. Alves et al., Simplified models for LHC new physics searches, J. Phys. G 39 (2012) 105005 [arXiv:1105.2838] [INSPIRE].

    ADS  Article  Google Scholar 

  15. [15]

    J. Alwall, P. Schuster and N. Toro, Simplified models for a first characterization of new physics at the LHC, Phys. Rev. D 79 (2009) 075020 [arXiv:0810.3921] [INSPIRE].

    ADS  Google Scholar 

  16. [16]

    D.S. Alves, E. Izaguirre and J.G. Wacker, Its on: early interpretations of ATLAS results in jets and missing energy searches, Phys. Lett. B 702 (2011) 64 [arXiv:1008.0407] [INSPIRE].

    ADS  Article  Google Scholar 

  17. [17]

    R. Essig, E. Izaguirre, J. Kaplan and J.G. Wacker, Heavy flavor simplified models at the LHC, JHEP 01 (2012) 074 [arXiv:1110.6443] [INSPIRE].

    ADS  Article  Google Scholar 

  18. [18]

    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].

    ADS  Google Scholar 

  19. [19]

    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].

    ADS  Google Scholar 

  20. [20]

    J. Andrea, B. Fuks and F. Maltoni, Monotops at the LHC, Phys. Rev. D 84 (2011) 074025 [arXiv:1106.6199] [INSPIRE].

    ADS  Google Scholar 

  21. [21]

    Y. Bai and T.M. Tait, Searches with mono-leptons, Phys. Lett. B 723 (2013) 384 [arXiv:1208.4361] [INSPIRE].

    ADS  Article  Google Scholar 

  22. [22]

    L.M. Carpenter, A. Nelson, C. Shimmin, T.M. Tait and D. Whiteson, Collider searches for dark matter in events with a Z boson and missing energy, arXiv:1212.3352 [INSPIRE].

  23. [23]

    T. Lin, E.W. Kolb and L.-T. Wang, Probing dark matter couplings to top and bottom at the LHC, Phys. Rev. D 88 (2013) 063510 [arXiv:1303.6638] [INSPIRE].

    ADS  Google Scholar 

  24. [24]

    DELPHI collaboration, J. Abdallah et al., Search for one large extra dimension with the DELPHI detector at LEP, Eur. Phys. J. C 60 (2009) 17 [arXiv:0901.4486] [INSPIRE].

    ADS  Article  Google Scholar 

  25. [25]

    ATLAS collaboration, Search for dark matter pair production in events with a hadronically decaying W or Z boson and missing transverse momentum in pp collision data at \( \sqrt{s} \) = 8 TeV with the ATLAS detector, ATLAS-CONF-2013-073, CERN, Geneva Switzerland (2013).

  26. [26]

    CMS collaboration, Search for dark matter in the mono-lepton channel with pp collision events at center-of-mass energy of 8 TeV, CMS-PAS-EXO-13-004, CERN, Geneva Switzerland (2013).

  27. [27]

    CMS collaboration, Search for invisible Higgs produced in association with a Z boson, CMS-PAS-HIG-13-018, CERN, Geneva Switzerland (2013).

  28. [28]

    ATLAS collaboration, Search for invisible decays of a Higgs boson produced in association with a Z boson in ATLAS, ATLAS-CONF-2013-011, CERN, Geneva Switzerland (2013).

  29. [29]

    ATLAS collaboration, Search for new phenomena in the dijet mass distribution updated using 13.0 fb−1 of pp collisions at \( \sqrt{s} \) = 8 TeV collected by the ATLAS detector, ATLAS-CONF-2012-148, CERN, Geneva Switzerland (2012).

  30. [30]

    CMS collaboration, Search for narrow resonances using the dijet mass spectrum in pp collisions at \( \sqrt{s} \) = 8 TeV, Phys. Rev. D 87 (2013) 114015 [arXiv:1302.4794] [INSPIRE].

    ADS  Google Scholar 

  31. [31]

    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].

    ADS  Article  Google Scholar 

  32. [32]

    P.J. Fox and C. Williams, Next-to-leading order predictions for dark matter production at hadron colliders, Phys. Rev. D 87 (2013) 054030 [arXiv:1211.6390] [INSPIRE].

    ADS  Google Scholar 

  33. [33]

    J. Alwall, M. Herquet, F. Maltoni, O. Mattelaer and T. Stelzer, MadGraph 5: going beyond, JHEP 06 (2011) 128 [arXiv:1106.0522] [INSPIRE].

    ADS  Article  Google Scholar 

  34. [34]

    T. Sjöstrand, S. Mrenna and P.Z. Skands, PYTHIA 6.4 physics and manual, JHEP 05 (2006) 026 [hep-ph/0603175] [INSPIRE].

    ADS  Article  Google Scholar 

  35. [35]

    J. Conway, Pretty Good Simulator webpage,∼conway/research/software/pgs/pgs4-general.htm.

  36. [36]

    S. Chang, R. Edezhath, J. Hutchinson and M. Luty, Effective WIMPs, arXiv:1307.8120 [INSPIRE].

  37. [37]

    H. An, L.-T. Wang and H. Zhang, Dark matter with t-channel mediator: a simple step beyond contact interaction, arXiv:1308.0592 [INSPIRE].

  38. [38]

    Y. Bai and J. Berger, Fermion portal dark matter, JHEP 11 (2013) 171 [arXiv:1308.0612] [INSPIRE].

    ADS  Article  Google Scholar 

  39. [39]

    A. DiFranzo, K.I. Nagao, A. Rajaraman and T.M.P. Tait, Simplified models for dark matter interacting with quarks, JHEP 11 (2013) 014 [arXiv:1308.2679] [INSPIRE].

    ADS  Article  Google Scholar 

  40. [40]

    B. Holdom, Two U(1)’s and ϵ charge shifts, Phys. Lett. B 166 (1986) 196 [INSPIRE].

    ADS  Article  Google Scholar 

  41. [41]

    K. Babu, C.F. Kolda and J. March-Russell, Implications of generalized Z-Z mixing, Phys. Rev. D 57 (1998) 6788 [hep-ph/9710441] [INSPIRE].

    ADS  Google Scholar 

  42. [42]

    R. Foadi, M.T. Frandsen and F. Sannino, Technicolor dark matter, Phys. Rev. D 80 (2009) 037702 [arXiv:0812.3406] [INSPIRE].

    ADS  Google Scholar 

  43. [43]

    H. An, R. Huo and L.-T. Wang, Searching for low mass dark portal at the LHC, Phys. Dark Univ. 2 (2013) 50 [arXiv:1212.2221] [INSPIRE].

    Article  Google Scholar 

  44. [44]

    H. An, X. Ji and L.-T. Wang, Light dark matter and Z dark force at colliders, JHEP 07 (2012) 182 [arXiv:1202.2894] [INSPIRE].

    ADS  Article  Google Scholar 

  45. [45]

    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].

    ADS  Article  Google Scholar 

  46. [46]

    Planck collaboration, P. Ade et al., Planck 2013 results. XVI. Cosmological parameters, arXiv:1303.5076 [INSPIRE].

  47. [47]

    C. Boehm and P. Fayet, Scalar dark matter candidates, Nucl. Phys. B 683 (2004) 219 [hep-ph/0305261] [INSPIRE].

    ADS  Article  Google Scholar 

  48. [48]

    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].

    ADS  Article  Google Scholar 

  49. [49]

    T. Cohen, D.J. Phalen and A. Pierce, On the correlation between the spin-independent and spin-dependent direct detection of dark matter, Phys. Rev. D 81 (2010) 116001 [arXiv:1001.3408] [INSPIRE].

    ADS  Google Scholar 

  50. [50]

    M. Freytsis and Z. Ligeti, On dark matter models with uniquely spin-dependent detection possibilities, Phys. Rev. D 83 (2011) 115009 [arXiv:1012.5317] [INSPIRE].

    ADS  Google Scholar 

  51. [51]

    G. Chalons, M.J. Dolan and C. McCabe, Neutralino dark matter and the Fermi gamma-ray lines, JCAP 02 (2013) 016 [arXiv:1211.5154] [INSPIRE].

    ADS  Article  Google Scholar 

  52. [52]

    HERMES collaboration, A. Airapetian et al., Precise determination of the spin structure function g 1 of the proton, deuteron and neutron, Phys. Rev. D 75 (2007) 012007 [hep-ex/0609039] [INSPIRE].

    ADS  Google Scholar 

  53. [53]

    S. Chang, A. Pierce and N. Weiner, Momentum dependent dark matter scattering, JCAP 01 (2010) 006 [arXiv:0908.3192] [INSPIRE].

    ADS  Article  Google Scholar 

  54. [54]

    M.T. Frandsen, F. Kahlhoefer, C. McCabe, S. Sarkar and K. Schmidt-Hoberg, The unbearable lightness of being: CDMS versus XENON, JCAP 07 (2013) 023 [arXiv:1304.6066] [INSPIRE].

    ADS  Article  Google Scholar 

  55. [55]

    XENON100 collaboration, E. Aprile et al., Limits on spin-dependent WIMP-nucleon cross sections from 225 live days of XENON100 data, Phys. Rev. Lett. 111 (2013) 021301 [arXiv:1301.6620] [INSPIRE].

    ADS  Article  Google Scholar 

  56. [56]

    COUPP collaboration, E. Behnke et al., First dark matter search results from a 4 kg CF 3 I bubble chamber operated in a deep underground site, Phys. Rev. D 86 (2012) 052001 [arXiv:1204.3094] [INSPIRE].

    ADS  Google Scholar 

  57. [57]

    M. Felizardo et al., Final analysis and results of the phase II SIMPLE dark matter search, Phys. Rev. Lett. 108 (2012) 201302 [arXiv:1106.3014] [INSPIRE].

    ADS  Article  Google Scholar 

  58. [58]

    PICASSO collaboration, S. Archambault et al., Constraints on low-mass WIMP interactions on 19 F from PICASSO, Phys. Lett. B 711 (2012) 153 [arXiv:1202.1240] [INSPIRE].

    ADS  Article  Google Scholar 

  59. [59]

    C. McCabe, The astrophysical uncertainties of dark matter direct detection experiments, Phys. Rev. D 82 (2010) 023530 [arXiv:1005.0579] [INSPIRE].

    ADS  Google Scholar 

  60. [60]

    Y.B. Zel’dovich, Magnetic model of universe, Zh. Eksp. Teor. Fiz. 48 (1965) 986.

  61. [61]

    Y.B. Zel’dovich, L.B. Okun and S.B. Pikelner, Quarks: the astrophysical and physical-chemistry aspects, Usp. Fiz. Nauk. 84 (1965) 113.

  62. [62]

    H.-Y. Chiu, Symmetry between particle and anti-particle populations in the universe, Phys. Rev. Lett. 17 (1966) 712 [INSPIRE].

    ADS  Article  Google Scholar 

  63. [63]

    C. Boehm, M.J. Dolan and C. McCabe, A lower bound on the mass of cold thermal dark matter from Planck, JCAP 08 (2013) 041 [arXiv:1303.6270] [INSPIRE].

    ADS  Article  Google Scholar 

  64. [64]

    K. Griest and M. Kamionkowski, Unitarity limits on the mass and radius of dark matter particles, Phys. Rev. Lett. 64 (1990) 615 [INSPIRE].

    ADS  Article  Google Scholar 

  65. [65]

    G. Steigman, Cosmology confronts particle physics, Ann. Rev. Nucl. Part. Sci. 29 (1979) 313 [INSPIRE].

    ADS  Article  Google Scholar 

  66. [66]

    J. Bernstein, L.S. Brown and G. Feinberg, The cosmological heavy neutrino problem revisited, Phys. Rev. D 32 (1985) 3261 [INSPIRE].

    ADS  Google Scholar 

  67. [67]

    R.J. Scherrer and M.S. Turner, On the relic, cosmic abundance of stable weakly interacting massive particles, Phys. Rev. D 33 (1986) 1585 [Erratum ibid. D 34 (1986) 3263] [INSPIRE].

    ADS  Google Scholar 

  68. [68]

    P. Gondolo and G. Gelmini, Cosmic abundances of stable particles: improved analysis, Nucl. Phys. B 360 (1991) 145 [INSPIRE].

    ADS  Article  Google Scholar 

  69. [69]

    E. Kolb and M. Turner, The early universe, Westview Press, Boulder U.S.A. (1990) [INSPIRE].

    MATH  Google Scholar 

  70. [70]

    M. Srednicki, R. Watkins and K.A. Olive, Calculations of relic densities in the early universe, Nucl. Phys. B 310 (1988) 693 [INSPIRE].

    ADS  Article  Google Scholar 

  71. [71]

    J.-M. Zheng et al., Constraining the interaction strength between dark matter and visible matter: i. Fermionic dark matter, Nucl. Phys. B 854 (2012) 350 [arXiv:1012.2022] [INSPIRE].

    ADS  Article  Google Scholar 

  72. [72]

    J. March-Russell, J. Unwin and S.M. West, Closing in on asymmetric dark matter I: model independent limits for interactions with quarks, JHEP 08 (2012) 029 [arXiv:1203.4854] [INSPIRE].

    ADS  Article  Google Scholar 

  73. [73]

    J. Goodman and W. Shepherd, LHC bounds on UV-complete models of dark matter, arXiv:1111.2359 [INSPIRE].

  74. [74]

    U. Haisch, F. Kahlhoefer and J. Unwin, The impact of heavy-quark loops on LHC dark matter searches, JHEP 07 (2013) 125 [arXiv:1208.4605] [INSPIRE].

    ADS  Article  Google Scholar 

  75. [75]

    J.F. Kamenik and J. Zupan, Discovering dark matter through flavor violation at the LHC, Phys. Rev. D 84 (2011) 111502 [arXiv:1107.0623] [INSPIRE].

    ADS  Google Scholar 

  76. [76]

    K. Cheung, K. Mawatari, E. Senaha, P.-Y. Tseng and T.-C. Yuan, The top window for dark matter, JHEP 10 (2010) 081 [arXiv:1009.0618] [INSPIRE].

    ADS  Article  Google Scholar 

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Buchmueller, O., Dolan, M.J. & McCabe, C. Beyond effective field theory for dark matter searches at the LHC. J. High Energ. Phys. 2014, 25 (2014).

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