Higgs portals for thermal Dark Matter. EFT perspectives and the NMSSM

  • Sebastian Baum
  • Marcela Carena
  • Nausheen R. Shah
  • Carlos E.M. Wagner
Open Access
Regular Article - Theoretical Physics


We analyze a low energy effective model of Dark Matter in which the thermal relic density is provided by a singlet Majorana fermion which interacts with the Higgs fields via higher dimensional operators. Direct detection signatures may be reduced if blind spot solutions exist, which naturally appear in models with extended Higgs sectors. Explicit mass terms for the Majorana fermion can be forbidden by a Z3 symmetry, which in addition leads to a reduction of the number of higher dimensional operators. Moreover, a weak scale mass for the Majorana fermion is naturally obtained from the vacuum expectation value of a scalar singlet field. The proper relic density may be obtained by the s-channel interchange of Higgs and gauge bosons, with the longitudinal mode of the Z boson (the neutral Goldstone mode) playing a relevant role in the annihilation process. This model shares many properties with the Next-to-Minimal Supersymmetric extension of the Standard Model (NMSSM) with light singlinos and heavy scalar and gauge superpartners. In order to test the validity of the low energy effective field theory, we compare its predictions with those of the ultraviolet complete NMSSM. Extending our framework to include Z3 neutral Majorana fermions, analogous to the bino in the NMSSM, we find the appearance of a new bino-singlino well tempered Dark Matter region.


Cosmology of Theories beyond the SM Beyond Standard Model Effective Field Theories Supersymmetric Effective Theories 


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]
    CRESST collaboration, G. Angloher et al., Results on light dark matter particles with a low-threshold CRESST-II detector, Eur. Phys. J. C 76 (2016) 25 [arXiv:1509.01515] [INSPIRE].
  2. [2]
    SuperCDMS collaboration, R. Agnese et al., Low-mass dark matter search with CDMSlite, Phys. Rev. D 97 (2018) 022002 [arXiv:1707.01632] [INSPIRE].
  3. [3]
    XENON collaboration, E. Aprile et al., First Dark Matter Search Results from the XENON1T Experiment, Phys. Rev. Lett. 119 (2017) 181301 [arXiv:1705.06655] [INSPIRE].
  4. [4]
    PandaX-II collaboration, X. Cui et al., Dark Matter Results From 54-Ton-Day Exposure of PandaX-II Experiment, Phys. Rev. Lett. 119 (2017) 181302 [arXiv:1708.06917] [INSPIRE].
  5. [5]
    LUX collaboration, D.S. Akerib et al., Limits on spin-dependent WIMP-nucleon cross section obtained from the complete LUX exposure, Phys. Rev. Lett. 118 (2017) 251302 [arXiv:1705.03380] [INSPIRE].
  6. [6]
    PICO collaboration, C. Amole et al., Dark Matter Search Results from the PICO-60 C 3 F 8 Bubble Chamber, Phys. Rev. Lett. 118 (2017) 251301 [arXiv:1702.07666] [INSPIRE].
  7. [7]
    M. Escudero, A. Berlin, D. Hooper and M.-X. Lin, Toward (Finally!) Ruling Out Z and Higgs Mediated Dark Matter Models, JCAP 12 (2016) 029 [arXiv:1609.09079] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    G.C. Branco, P.M. Ferreira, L. Lavoura, M.N. Rebelo, M. Sher and J.P. Silva, Theory and phenomenology of two-Higgs-doublet models, Phys. Rept. 516 (2012) 1 [arXiv:1106.0034] [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    S. Kanemura, S. Matsumoto, T. Nabeshima and N. Okada, Can WIMP Dark Matter overcome the Nightmare Scenario?, Phys. Rev. D 82 (2010) 055026 [arXiv:1005.5651] [INSPIRE].ADSGoogle Scholar
  10. [10]
    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].ADSCrossRefGoogle Scholar
  11. [11]
    O. Lebedev, H.M. Lee and Y. Mambrini, Vector Higgs-portal dark matter and the invisible Higgs, Phys. Lett. B 707 (2012) 570 [arXiv:1111.4482] [INSPIRE].ADSCrossRefGoogle Scholar
  12. [12]
    C.-F. Chang, X.-G. He and J. Tandean, Two-Higgs-Doublet-Portal Dark-Matter Models in Light of Direct Search and LHC Data, JHEP 04 (2017) 107 [arXiv:1702.02924] [INSPIRE].ADSGoogle Scholar
  13. [13]
    M. Perelstein and B. Shakya, XENON100 implications for naturalness in the MSSM, NMSSM and λ-supersymmetry model, Phys. Rev. D 88 (2013) 075003 [arXiv:1208.0833] [INSPIRE].ADSGoogle Scholar
  14. [14]
    C. Cheung, L.J. Hall, D. Pinner and J.T. Ruderman, Prospects and Blind Spots for Neutralino Dark Matter, JHEP 05 (2013) 100 [arXiv:1211.4873] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    P. Huang and C.E.M. Wagner, Blind Spots for neutralino Dark Matter in the MSSM with an intermediate m A, Phys. Rev. D 90 (2014) 015018 [arXiv:1404.0392] [INSPIRE].ADSGoogle Scholar
  16. [16]
    C. Cheung, M. Papucci, D. Sanford, N.R. Shah and K.M. Zurek, NMSSM Interpretation of the Galactic Center Excess, Phys. Rev. D 90 (2014) 075011 [arXiv:1406.6372] [INSPIRE].ADSGoogle Scholar
  17. [17]
    T. Han, F. Kling, S. Su and Y. Wu, Unblinding the dark matter blind spots, JHEP 02 (2017) 057 [arXiv:1612.02387] [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    P. Huang, R.A. Roglans, D.D. Spiegel, Y. Sun and C.E.M. Wagner, Constraints on Supersymmetric Dark Matter for Heavy Scalar Superpartners, Phys. Rev. D 95 (2017) 095021 [arXiv:1701.02737] [INSPIRE].ADSGoogle Scholar
  19. [19]
    M. Badziak, M. Olechowski and P. Szczerbiak, Spin-dependent constraints on blind spots for thermal singlino-higgsino dark matter with(out) light singlets, JHEP 07 (2017) 050 [arXiv:1705.00227] [INSPIRE].ADSGoogle Scholar
  20. [20]
    S.P. Martin, A supersymmetry primer, hep-ph/9709356 [INSPIRE].
  21. [21]
    H.P. Nilles, Supersymmetry, Supergravity and Particle Physics, Phys. Rept. 110 (1984) 1 [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    H.E. Haber and G.L. Kane, The Search for Supersymmetry: Probing Physics Beyond the Standard Model, Phys. Rept. 117 (1985) 75 [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    J.A. Casas, J.R. Espinosa, M. Quirós and A. Riotto, The lightest Higgs boson mass in the minimal supersymmetric standard model, Nucl. Phys. B 436 (1995) 3 [Erratum ibid. B 439 (1995) 466] [hep-ph/9407389] [INSPIRE].
  24. [24]
    H.E. Haber, R. Hempfling and A.H. Hoang, Approximating the radiatively corrected Higgs mass in the minimal supersymmetric model, Z. Phys. C 75 (1997) 539 [hep-ph/9609331] [INSPIRE].
  25. [25]
    G. Degrassi, S. Heinemeyer, W. Hollik, P. Slavich and G. Weiglein, Towards high precision predictions for the MSSM Higgs sector, Eur. Phys. J. C 28 (2003) 133 [hep-ph/0212020] [INSPIRE].
  26. [26]
    U. Ellwanger, C. Hugonie and A.M. Teixeira, The Next-to-Minimal Supersymmetric Standard Model, Phys. Rept. 496 (2010) 1 [arXiv:0910.1785] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  27. [27]
    Z. Kang, J. Li, T. Li, D. Liu and J. Shu, Probing the CP-even Higgs sector via H 3H 2 H 1 in the natural next-to-minimal supersymmetric standard model, Phys. Rev. D 88 (2013) 015006 [arXiv:1301.0453] [INSPIRE].ADSGoogle Scholar
  28. [28]
    S.F. King, M. Mühlleitner, R. Nevzorov and K. Walz, Discovery Prospects for NMSSM Higgs Bosons at the High-Energy Large Hadron Collider, Phys. Rev. D 90 (2014) 095014 [arXiv:1408.1120] [INSPIRE].ADSGoogle Scholar
  29. [29]
    M. Carena, H.E. Haber, I. Low, N.R. Shah and C.E.M. Wagner, Alignment limit of the NMSSM Higgs sector, Phys. Rev. D 93 (2016) 035013 [arXiv:1510.09137] [INSPIRE].ADSGoogle Scholar
  30. [30]
    U. Ellwanger and M. Rodriguez-Vazquez, Discovery Prospects of a Light Scalar in the NMSSM, JHEP 02 (2016) 096 [arXiv:1512.04281] [INSPIRE].ADSCrossRefGoogle Scholar
  31. [31]
    R. Costa, M. Mühlleitner, M.O.P. Sampaio and R. Santos, Singlet Extensions of the Standard Model at LHC Run 2: Benchmarks and Comparison with the NMSSM, JHEP 06 (2016) 034 [arXiv:1512.05355] [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    S. Baum, K. Freese, N.R. Shah and B. Shakya, NMSSM Higgs boson search strategies at the LHC and the mono-Higgs signature in particular, Phys. Rev. D 95 (2017) 115036 [arXiv:1703.07800] [INSPIRE].ADSGoogle Scholar
  33. [33]
    U. Ellwanger and M. Rodriguez-Vazquez, Simultaneous search for extra light and heavy Higgs bosons via cascade decays, JHEP 11 (2017) 008 [arXiv:1707.08522] [INSPIRE].ADSCrossRefGoogle Scholar
  34. [34]
    H. Georgi and D.V. Nanopoulos, Suppression of Flavor Changing Effects From Neutral Spinless Meson Exchange in Gauge Theories, Phys. Lett. B 82 (1979) 95 [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    J.F. Donoghue and L.F. Li, Properties of Charged Higgs Bosons, Phys. Rev. D 19 (1979) 945 [INSPIRE].ADSGoogle Scholar
  36. [36]
    J. Gunion, H. Haber, G. Kane and S. Dawson, The Higgs Hunter’s Guide, Frontiers in Physics, Westview Press, (2008).Google Scholar
  37. [37]
    L. Lavoura and J.P. Silva, Fundamental CP-violating quantities in a SU(2) × U(1) model with many Higgs doublets, Phys. Rev. D 50 (1994) 4619 [hep-ph/9404276] [INSPIRE].
  38. [38]
    F.J. Botella and J.P. Silva, Jarlskog-like invariants for theories with scalars and fermions, Phys. Rev. D 51 (1995) 3870 [hep-ph/9411288] [INSPIRE].
  39. [39]
    G.C. Branco, L. Lavoura and S.J.P., CP violation, Oxford University Press, Oxford, U.K., (1999).Google Scholar
  40. [40]
    J.F. Gunion and H.E. Haber, The CP conserving two Higgs doublet model: The approach to the decoupling limit, Phys. Rev. D 67 (2003) 075019 [hep-ph/0207010] [INSPIRE].
  41. [41]
    ATLAS and CMS collaborations, Combined Measurement of the Higgs Boson Mass in pp Collisions at \( \sqrt{s}=7 \) and 8 TeV with the ATLAS and CMS Experiments, Phys. Rev. Lett. 114 (2015) 191803 [arXiv:1503.07589] [INSPIRE].
  42. [42]
    ATLAS and 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, JHEP 08 (2016) 045 [arXiv:1606.02266] [INSPIRE].
  43. [43]
    Planck collaboration, P.A.R. Ade et al., Planck 2015 results. XIII. Cosmological parameters, Astron. Astrophys. 594 (2016) A13 [arXiv:1502.01589] [INSPIRE].
  44. [44]
    G. Bélanger, F. Boudjema, A. Pukhov and A. Semenov, MicrOMEGAs 3: A program for calculating dark matter observables, Comput. Phys. Commun. 185 (2014) 960 [arXiv:1305.0237] [INSPIRE].ADSCrossRefGoogle Scholar
  45. [45]
    G. Bélanger, F. Boudjema, A. Pukhov and A. Semenov, MicrOMEGAs: A tool for dark matter studies, Nuovo Cim. C 033N2 (2010) 111 [arXiv:1005.4133] [INSPIRE].
  46. [46]
    G. Bélanger, F. Boudjema, A. Pukhov and A. Semenov, Dark matter direct detection rate in a generic model with MicrOMEGAs 2.2, Comput. Phys. Commun. 180 (2009) 747 [arXiv:0803.2360] [INSPIRE].
  47. [47]
    G. Bélanger, F. Boudjema, A. Pukhov and A. Semenov, MicrOMEGAs 2.0: A program to calculate the relic density of dark matter in a generic model, Comput. Phys. Commun. 176 (2007) 367 [hep-ph/0607059] [INSPIRE].
  48. [48]
    M. Maniatis, The Next-to-Minimal Supersymmetric extension of the Standard Model reviewed, Int. J. Mod. Phys. A 25 (2010) 3505 [arXiv:0906.0777] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  49. [49]
    T. Gherghetta, B. von Harling, A.D. Medina and M.A. Schmidt, The Scale-Invariant NMSSM and the 126 GeV Higgs Boson, JHEP 02 (2013) 032 [arXiv:1212.5243] [INSPIRE].ADSCrossRefGoogle Scholar
  50. [50]
    N.D. Christensen, T. Han, Z. Liu and S. Su, Low-Mass Higgs Bosons in the NMSSM and Their LHC Implications, JHEP 08 (2013) 019 [arXiv:1303.2113] [INSPIRE].ADSCrossRefGoogle Scholar
  51. [51]
    B. Dutta, Y. Gao and B. Shakya, Light Higgsino Decays as a Probe of the NMSSM, Phys. Rev. D 91 (2015) 035016 [arXiv:1412.2774] [INSPIRE].ADSGoogle Scholar
  52. [52]
    J. Cao, Y. He, L. Shang, W. Su and Y. Zhang, Natural NMSSM after LHC Run I and the Higgsino dominated dark matter scenario, JHEP 08 (2016) 037 [arXiv:1606.04416] [INSPIRE].ADSCrossRefGoogle Scholar
  53. [53]
    U. Ellwanger, Present Status and Future Tests of the Higgsino-Singlino Sector in the NMSSM, JHEP 02 (2017) 051 [arXiv:1612.06574] [INSPIRE].ADSCrossRefGoogle Scholar
  54. [54]
    J. Cao, L. Shang, P. Wu, J.M. Yang and Y. Zhang, Interpreting the galactic center gamma-ray excess in the NMSSM, JHEP 10 (2015) 030 [arXiv:1506.06471] [INSPIRE].ADSCrossRefGoogle Scholar
  55. [55]
    M. Badziak, M. Olechowski and P. Szczerbiak, Blind spots for neutralino dark matter in the NMSSM, JHEP 03 (2016) 179 [arXiv:1512.02472] [INSPIRE].ADSCrossRefGoogle Scholar
  56. [56]
    J. Cao, Y. He, L. Shang, W. Su, P. Wu and Y. Zhang, Strong constraints of LUX-2016 results on the natural NMSSM, JHEP 10 (2016) 136 [arXiv:1609.00204] [INSPIRE].ADSCrossRefGoogle Scholar
  57. [57]
    C. Beskidt, W. de Boer, D.I. Kazakov and S. Wayand, Perspectives of direct Detection of supersymmetric Dark Matter in the NMSSM, Phys. Lett. B 771 (2017) 611 [arXiv:1703.01255] [INSPIRE].ADSCrossRefGoogle Scholar
  58. [58]
  59. [59]
    U. Ellwanger, J.F. Gunion and C. Hugonie, NMHDECAY: A Fortran code for the Higgs masses, couplings and decay widths in the NMSSM, JHEP 02 (2005) 066 [hep-ph/0406215] [INSPIRE].
  60. [60]
    U. Ellwanger and C. Hugonie, NMHDECAY 2.0: An updated program for sparticle masses, Higgs masses, couplings and decay widths in the NMSSM, Comput. Phys. Commun. 175 (2006) 290 [hep-ph/0508022] [INSPIRE].
  61. [61]
    D. Das, U. Ellwanger and A.M. Teixeira, NMSDECAY: A Fortran Code for Supersymmetric Particle Decays in the Next-to-Minimal Supersymmetric Standard Model, Comput. Phys. Commun. 183 (2012) 774 [arXiv:1106.5633] [INSPIRE].ADSCrossRefGoogle Scholar
  62. [62]
    M. Mühlleitner, A. Djouadi and Y. Mambrini, SDECAY: A Fortran code for the decays of the supersymmetric particles in the MSSM, Comput. Phys. Commun. 168 (2005) 46 [hep-ph/0311167] [INSPIRE].
  63. [63]
    G. Bélanger, F. Boudjema, C. Hugonie, A. Pukhov and A. Semenov, Relic density of dark matter in the NMSSM, JCAP 09 (2005) 001 [hep-ph/0505142] [INSPIRE].
  64. [64]
    U. Ellwanger and C. Hugonie, NMSPEC: A Fortran code for the sparticle and Higgs masses in the NMSSM with GUT scale boundary conditions, Comput. Phys. Commun. 177 (2007) 399 [hep-ph/0612134] [INSPIRE].
  65. [65]
    K. Griest and D. Seckel, Three exceptions in the calculation of relic abundances, Phys. Rev. D 43 (1991) 3191 [INSPIRE].ADSGoogle Scholar
  66. [66]
    P. Bergeron, P. Sandick and K. Sinha, Theoretical Uncertainties in the Calculation of Supersymmetric Dark Matter Observables, arXiv:1712.05491 [INSPIRE].
  67. [67]
    M.D. Goodsell, K. Nickel and F. Staub, Two-loop corrections to the Higgs masses in the NMSSM, Phys. Rev. D 91 (2015) 035021 [arXiv:1411.4665] [INSPIRE].ADSGoogle Scholar
  68. [68]
    F. Staub et al., Higgs mass predictions of public NMSSM spectrum generators, Comput. Phys. Commun. 202 (2016) 113 [arXiv:1507.05093] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  69. [69]
    Fermi-LAT and MAGIC collaborations, M.L. Ahnen et al., Limits to dark matter annihilation cross-section from a combined analysis of MAGIC and Fermi-LAT observations of dwarf satellite galaxies, JCAP 02 (2016) 039 [arXiv:1601.06590] [INSPIRE].
  70. [70]
    DES and Fermi-LAT collaborations, A. Albert et al., Searching for Dark Matter Annihilation in Recently Discovered Milky Way Satellites with Fermi-LAT, Astrophys. J. 834 (2017) 110 [arXiv:1611.03184] [INSPIRE].
  71. [71]
    S. Baum, L. Visinelli, K. Freese and P. Stengel, Dark matter capture, subdominant WIMPs and neutrino observatories, Phys. Rev. D 95 (2017) 043007 [arXiv:1611.09665] [INSPIRE].ADSGoogle Scholar
  72. [72]
    Super-Kamiokande collaboration, T. Tanaka et al., An Indirect Search for WIMPs in the Sun using 3109.6 days of upward-going muons in Super-Kamiokande, Astrophys. J. 742 (2011) 78 [arXiv:1108.3384] [INSPIRE].
  73. [73]
    Super-Kamiokande collaboration, K. Choi et al., Search for neutrinos from annihilation of captured low-mass dark matter particles in the Sun by Super-Kamiokande, Phys. Rev. Lett. 114 (2015) 141301 [arXiv:1503.04858] [INSPIRE].
  74. [74]
    IceCube collaboration, R. Abbasi et al., Multi-year search for dark matter annihilations in the Sun with the AMANDA-II and IceCube detectors, Phys. Rev. D 85 (2012) 042002 [arXiv:1112.1840] [INSPIRE].
  75. [75]
    IceCube collaboration, M.G. Aartsen et al., Improved limits on dark matter annihilation in the Sun with the 79-string IceCube detector and implications for supersymmetry, JCAP 04 (2016) 022 [arXiv:1601.00653] [INSPIRE].
  76. [76]
    J.D. Zornoza and C. Toennis, Results of dark matter searches with the ANTARES neutrino telescope, J. Phys. Conf. Ser. 888 (2017) 012206 [arXiv:1611.02555] [INSPIRE].CrossRefGoogle Scholar
  77. [77]
    Fermi-LAT collaboration, V. Vitale and A. Morselli, Indirect Search for Dark Matter from the center of the Milky Way with the Fermi-Large Area Telescope, in Fermi gamma-ray space telescope. Proceedings, 2nd Fermi Symposium, Washington, U.S.A., November 2-5, 2009, arXiv:0912.3828 [INSPIRE].
  78. [78]
    L. Goodenough and D. Hooper, Possible Evidence For Dark Matter Annihilation In The Inner Milky Way From The Fermi Gamma Ray Space Telescope, arXiv:0910.2998 [INSPIRE].
  79. [79]
    Fermi-LAT collaboration, M. Ackermann et al., The Fermi Galactic Center GeV Excess and Implications for Dark Matter, Astrophys. J. 840 (2017) 43 [arXiv:1704.03910] [INSPIRE].
  80. [80]
    K. Freese, A. Lopez, N.R. Shah and B. Shakya, MSSM A-funnel and the Galactic Center Excess: Prospects for the LHC and Direct Detection Experiments, JHEP 04 (2016) 059 [arXiv:1509.05076] [INSPIRE].ADSGoogle Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

  • Sebastian Baum
    • 1
    • 2
  • Marcela Carena
    • 3
    • 4
  • Nausheen R. Shah
    • 5
  • Carlos E.M. Wagner
    • 4
    • 6
  1. 1.The Oskar Klein Centre for Cosmoparticle Physics, Department of PhysicsStockholm UniversityStockholmSweden
  2. 2.Nordita, KTH Royal Institute of Technology and Stockholm UniversityStockholmSweden
  3. 3.Fermi National Accelerator LaboratoryBataviaU.S.A.
  4. 4.Enrico Fermi Institute and Kavli Institute for Cosmological PhysicsUniversity of ChicagoChicagoU.S.A.
  5. 5.Department of Physics & AstronomyWayne State UniversityDetroitU.S.A.
  6. 6.HEP DivisionArgonne National LaboratoryArgonneU.S.A.

Personalised recommendations