# Dark matter in the inert doublet model after the discovery of a Higgs-like boson at the LHC

## Abstract

We examine the Inert Doublet Model in light of the discovery of a Higgs-like boson with a mass of roughly 126 GeV at the LHC. We evaluate one-loop corrections to the scalar masses and perform a numerical solution of the one-loop renormalization group equations. Demanding vacuum stability, perturbativity, and *S*-matrix unitarity, we compute the scale up to which the model can be extrapolated. From this we derive constraints on the model parameters in the presence of a 126 GeV Higgs boson. We perform an improved calculation of the dark matter relic density with the Higgs mass fixed to the measured value, taking into account the effects of three- and four-body final states resulting from off-shell production of gauge bosons in dark matter annihilation. Issues related to direct detection of dark matter are discussed, in particular the role of hadronic uncertainties. The predictions for the interesting decay mode *h* ^{0} → *γγ* are presented for scenarios which fulfill all model constraints, and we discuss how a potential enhancement of this rate from the charged inert scalar is related to the properties of dark matter in this model. We also apply LHC limits on Higgs boson decays to invisible final states, which provide additional constraints on the mass of the dark matter candidate. Finally, we propose three benchmark points that capture different aspects of the relevant phenomenology.

## Keywords

Higgs Physics Beyond Standard Model Cosmology of Theories beyond the SM GUT## References

- [1]N.G. Deshpande and E. Ma,
*Pattern of symmetry breaking with two Higgs doublets*,*Phys. Rev.***D 18**(1978) 2574 [INSPIRE].ADSGoogle Scholar - [2]E. Ma,
*Verifiable radiative seesaw mechanism of neutrino mass and dark matter*,*Phys. Rev.***D 73**(2006) 077301 [hep-ph/0601225] [INSPIRE].ADSGoogle Scholar - [3]R. Barbieri, L.J. Hall and V.S. Rychkov,
*Improved naturalness with a heavy Higgs: an alternative road to LHC physics*,*Phys. Rev.***D 74**(2006) 015007 [hep-ph/0603188] [INSPIRE].ADSGoogle Scholar - [4]M. Gustafsson, E. Lundström, L. Bergström and J. Edsjö,
*Significant*Γ*lines from inert Higgs dark matter*,*Phys. Rev. Lett.***99**(2007) 041301 [astro-ph/0703512] [INSPIRE].ADSCrossRefGoogle Scholar - [5]P. Agrawal, E.M. Dolle and C.A. Krenke,
*Signals of inert doublet dark matter in neutrino telescopes*,*Phys. Rev.***D 79**(2009) 015015 [arXiv:0811.1798] [INSPIRE].ADSGoogle Scholar - [6]S. Andreas, M.H. Tytgat and Q. Swillens,
*Neutrinos from inert doublet dark matter*,*JCAP***04**(2009) 004 [arXiv:0901.1750] [INSPIRE].ADSCrossRefGoogle Scholar - [7]E. Nezri, M.H. Tytgat and G. Vertongen,
*e*^{+}*and*\( \overline{p} \)*from inert doublet model dark matter*,*JCAP***04**(2009) 014 [arXiv:0901.2556] [INSPIRE].ADSCrossRefGoogle Scholar - [8]C. Arina, F.-S. Ling and M.H. Tytgat,
*IDM and iDM or the inert doublet model and inelastic dark matter*,*JCAP***10**(2009) 018 [arXiv:0907.0430] [INSPIRE].ADSCrossRefGoogle Scholar - [9]J.-O. Gong, H.M. Lee and S.K. Kang,
*Inflation and dark matter in two Higgs doublet models*,*JHEP***04**(2012) 128 [arXiv:1202.0288] [INSPIRE].ADSCrossRefGoogle Scholar - [10]L. Lopez Honorez, E. Nezri, J.F. Oliver and M.H. Tytgat,
*The inert doublet model: an archetype for dark matter*,*JCAP***02**(2007) 028 [hep-ph/0612275] [INSPIRE].ADSCrossRefGoogle Scholar - [11]WMAP collaboration, E. Komatsu et al.,
*Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: cosmological interpretation*,*Astrophys. J. Suppl.***192**(2011) 18 [arXiv:1001.4538] [INSPIRE].ADSCrossRefGoogle Scholar - [12]M. Gustafsson, S. Rydbeck, L. Lopez-Honorez and E. Lundstrom,
*Status of the inert doublet model and the role of multileptons at the LHC*,*Phys. Rev.***D 86**(2012) 075019 [arXiv:1206.6316] [INSPIRE].ADSGoogle Scholar - [13]E. Lundström, M. Gustafsson and J. Edsjö,
*The inert doublet model and LEP II limits*,*Phys. Rev.***D 79**(2009) 035013 [arXiv:0810.3924] [INSPIRE].ADSGoogle Scholar - [14]Q.-H. Cao, E. Ma and G. Rajasekaran,
*Observing the dark scalar doublet and its impact on the standard-model Higgs boson at colliders*,*Phys. Rev.***D 76**(2007) 095011 [arXiv:0708.2939] [INSPIRE].ADSGoogle Scholar - [15]E. Dolle, X. Miao, S. Su and B. Thomas,
*Dilepton signals in the inert doublet model*,*Phys. Rev.***D 81**(2010) 035003 [arXiv:0909.3094] [INSPIRE].ADSGoogle Scholar - [16]X. Miao, S. Su and B. Thomas,
*Trilepton signals in the inert doublet model*,*Phys. Rev.***D 82**(2010) 035009 [arXiv:1005.0090] [INSPIRE].ADSGoogle Scholar - [17]L. Wang and X.-F. Han,
*LHC diphoton Higgs signal and top quark forward-backward asymmetry in quasi-inert Higgs doublet model*,*JHEP***05**(2012) 088 [arXiv:1203.4477] [INSPIRE].ADSCrossRefGoogle Scholar - [18]P. Osland, A. Pukhov, G. Pruna and M. Purmohammadi,
*Phenomenology of charged scalars in the CP-violating inert-doublet model*,*JHEP***04**(2013) 040 [arXiv:1302.3713] [INSPIRE].ADSCrossRefGoogle Scholar - [19]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].ADSGoogle Scholar - [20]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].ADSGoogle Scholar - [21]Tevatron New Physics Higgs Working Group, CDF, D0 collaboration,
*Updated combination of CDF and D0 searches for standard model Higgs boson production with up to*10*.*0*fb*^{−1}*of data*, arXiv:1207.0449 [INSPIRE]. - [22]T. Hambye and M.H. Tytgat,
*Electroweak symmetry breaking induced by dark matter*,*Phys. Lett.***B 659**(2008) 651 [arXiv:0707.0633] [INSPIRE].ADSCrossRefGoogle Scholar - [23]M. Klasen, C.E. Yaguna and J.D. Ruiz-Alvarez,
*Electroweak corrections to the direct detection cross section of inert Higgs dark matter*,*Phys. Rev.***D 87**(2013) 075025 [arXiv:1302.1657] [INSPIRE].ADSGoogle Scholar - [24]G. Branco et al.,
*Theory and phenomenology of two-Higgs-doublet models*,*Phys. Rept.***516**(2012) 1 [arXiv:1106.0034] [INSPIRE].ADSCrossRefGoogle Scholar - [25]T.A. Chowdhury, M. Nemevšek, G. Senjanović and Y. Zhang,
*Dark matter as the trigger of strong electroweak phase transition*,*JCAP***02**(2012) 029 [arXiv:1110.5334] [INSPIRE].ADSCrossRefGoogle Scholar - [26]D. Borah and J.M. Cline,
*Inert doublet dark matter with strong electroweak phase transition*,*Phys. Rev.***D 86**(2012) 055001 [arXiv:1204.4722] [INSPIRE].ADSGoogle Scholar - [27]J.M. Cline and K. Kainulainen,
*Improved electroweak phase transition with subdominant inert doublet dark matter*,*Phys. Rev.***D 87**(2013) 071701 [arXiv:1302.2614] [INSPIRE].ADSGoogle Scholar - [28]M. Drees, J. Kim and K. Nagao,
*Potentially large one-loop corrections to WIMP annihilation*,*Phys. Rev.***D 81**(2010) 105004 [arXiv:0911.3795] [INSPIRE].ADSGoogle Scholar - [29]A. Freitas,
*Radiative corrections to co-annihilation processes*,*Phys. Lett.***B 652**(2007) 280 [arXiv:0705.4027] [INSPIRE].ADSCrossRefGoogle Scholar - [30]B. Herrmann and M. Klasen,
*SUSY-QCD corrections to dark matter annihilation in the Higgs funnel*,*Phys. Rev.***D 76**(2007) 117704 [arXiv:0709.0043] [INSPIRE].ADSGoogle Scholar - [31]B. Herrmann, M. Klasen and K. Kovarik,
*Neutralino annihilation into massive quarks with SUSY-QCD corrections*,*Phys. Rev.***D 79**(2009) 061701 [arXiv:0901.0481] [INSPIRE].ADSGoogle Scholar - [32]B. Herrmann, M. Klasen and K. Kovarik,
*SUSY-QCD effects on neutralino dark matter annihilation beyond scalar or gaugino mass unification*,*Phys. Rev.***D 80**(2009) 085025 [arXiv:0907.0030] [INSPIRE].ADSGoogle Scholar - [33]J. Harz, B. Herrmann, M. Klasen, K. Kovarik and Q.L. Boulc’h,
*Neutralino-stop co-annihilation into electroweak gauge and Higgs bosons at one loop*,*Phys. Rev.***D 87**(2013) 054031 [arXiv:1212.5241] [INSPIRE]. - [34]N. Baro, F. Boudjema and A. Semenov,
*Full one-loop corrections to the relic density in the MSSM: a few examples*,*Phys. Lett.***B 660**(2008) 550 [arXiv:0710.1821] [INSPIRE].ADSCrossRefGoogle Scholar - [35]N. Baro, F. Boudjema, G. Chalons and S. Hao,
*Relic density at one-loop with gauge boson pair production*,*Phys. Rev.***D 81**(2010) 015005 [arXiv:0910.3293] [INSPIRE].ADSGoogle Scholar - [36]F. Boudjema, G. Drieu La Rochelle and S. Kulkarni,
*One-loop corrections, uncertainties and approximations in neutralino annihilations: examples*,*Phys. Rev.***D 84**(2011) 116001 [arXiv:1108.4291] [INSPIRE].ADSGoogle Scholar - [37]T. Hambye, F.-S. Ling, L. Lopez Honorez and J. Rocher,
*Scalar multiplet dark matter*,*JHEP***07**(2009) 090 [*Erratum ibid.***1005**(2010) 066] [arXiv:0903.4010] [INSPIRE]. - [38]L. Lopez Honorez and C.E. Yaguna,
*The inert doublet model of dark matter revisited*,*JHEP***09**(2010) 046 [arXiv:1003.3125] [INSPIRE].ADSCrossRefGoogle Scholar - [39]L. Lopez Honorez and C.E. Yaguna,
*A new viable region of the inert doublet model*,*JCAP***01**(2011) 002 [arXiv:1011.1411] [INSPIRE].ADSGoogle Scholar - [40]XENON100 collaboration, E. Aprile et al.,
*Dark matter results from 225 live days of XENON100 data*,*Phys. Rev. Lett.***109**(2012) 181301 [arXiv:1207.5988] [INSPIRE].ADSCrossRefGoogle Scholar - [41]F. Staub, W. Porod and B. Herrmann,
*The electroweak sector of the NMSSM at the one-loop level*,*JHEP***10**(2010) 040 [arXiv:1007.4049] [INSPIRE].ADSCrossRefGoogle Scholar - [42]T. Hahn,
*Generating Feynman diagrams and amplitudes with FeynArts 3*,*Comput. Phys. Commun.***140**(2001) 418 [hep-ph/0012260] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar - [43]N.D. Christensen and C. Duhr,
*FeynRules*—*Feynman rules made easy*,*Comput. Phys. Commun.***180**(2009) 1614 [arXiv:0806.4194] [INSPIRE].ADSCrossRefGoogle Scholar - [44]
- [45]F. Staub,
*From superpotential to model files for FeynArts and CalcHep/CompHEP*,*Comput. Phys. Commun.***181**(2010) 1077 [arXiv:0909.2863] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar - [46]F. Staub,
*Automatic calculation of supersymmetric renormalization group equations and self energies*,*Comput. Phys. Commun.***182**(2011) 808 [arXiv:1002.0840] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar - [47]A. Denner,
*Techniques for calculation of electroweak radiative corrections at the one loop level and results for W physics at LEP-200*,*Fortsch. Phys.***41**(1993) 307 [arXiv:0709.1075] [INSPIRE].ADSCrossRefGoogle Scholar - [48]M. Gonderinger, Y. Li, H. Patel and M.J. Ramsey-Musolf,
*Vacuum stability, perturbativity and scalar singlet dark matter*,*JHEP***01**(2010) 053 [arXiv:0910.3167] [INSPIRE].ADSCrossRefGoogle Scholar - [49]K. Inoue, A. Kakuto and Y. Nakano,
*Perturbation constraint on particle masses in the Weinberg-Salam model with two massless Higgs doublets*,*Prog. Theor. Phys.***63**(1980) 234 [INSPIRE].ADSCrossRefGoogle Scholar - [50]P. Ferreira and D. Jones,
*Bounds on scalar masses in two Higgs doublet models*,*JHEP***08**(2009) 069 [arXiv:0903.2856] [INSPIRE].ADSCrossRefGoogle Scholar - [51]M. Gustafsson,
*The inert doublet model and its phenomenology*, PoS(CHARGED 2010)030 [arXiv:1106.1719] [INSPIRE]. - [52]B. Swiezewska,
*Yukawa independent constraints for 2HDMs with a*125*GeV Higgs boson*, arXiv:1209.5725 [INSPIRE]. - [53]J. Elias-Miro et al.,
*Higgs mass implications on the stability of the electroweak vacuum*,*Phys. Lett.***B 709**(2012) 222 [arXiv:1112.3022] [INSPIRE].ADSCrossRefGoogle Scholar - [54]M. Sher,
*Electroweak Higgs potentials and vacuum stability*,*Phys. Rept.***179**(1989) 273 [INSPIRE].ADSCrossRefGoogle Scholar - [55]H. Huffel and G. Pocsik,
*Unitarity bounds on Higgs boson masses in the Weinberg-Salam model with two Higgs doublets*,*Z. Phys.***C 8**(1981) 13 [INSPIRE].ADSGoogle Scholar - [56]J. Maalampi, J. Sirkka and I. Vilja,
*Tree level unitarity and triviality bounds for two Higgs models*,*Phys. Lett.***B 265**(1991) 371 [INSPIRE].ADSCrossRefGoogle Scholar - [57]I. Ginzburg and I. Ivanov,
*Tree-level unitarity constraints in the most general 2HDM*,*Phys. Rev.***D 72**(2005) 115010 [hep-ph/0508020] [INSPIRE].ADSGoogle Scholar - [58]G. Altarelli and R. Barbieri,
*Vacuum polarization effects of new physics on electroweak processes*,*Phys. Lett.***B 253**(1991) 161 [INSPIRE].ADSCrossRefGoogle Scholar - [59]M.E. Peskin and T. Takeuchi,
*Estimation of oblique electroweak corrections*,*Phys. Rev.***D 46**(1992) 381 [INSPIRE].ADSGoogle Scholar - [60]M. Baak et al.,
*Updated status of the global electroweak fit and constraints on new physics*,*Eur. Phys. J.***C 72**(2012) 2003 [arXiv:1107.0975] [INSPIRE].ADSCrossRefGoogle Scholar - [61]A. Pierce and J. Thaler,
*Natural dark matter from an unnatural Higgs boson and new colored particles at the TeV scale*,*JHEP***08**(2007) 026 [hep-ph/0703056] [INSPIRE].ADSCrossRefGoogle Scholar - [62]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].ADSCrossRefzbMATHGoogle Scholar - [63]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].ADSCrossRefzbMATHGoogle Scholar - [64]G. Belanger, F. Boudjema, A. Pukhov and A. Semenov,
*micrOMEGAs3.1 : a program for calculating dark matter observables*, arXiv:1305.0237 [INSPIRE]. - [65]XENON10 collaboration, J. Angle et al.,
*A search for light dark matter in XENON10 data*,*Phys. Rev. Lett.***107**(2011) 051301 [arXiv:1104.3088] [INSPIRE].ADSCrossRefGoogle Scholar - [66]XENON100 collaboration, E. Aprile et al.,
*Dark matter results from 100 live days of XENON100 data*,*Phys. Rev. Lett.***107**(2011) 131302 [arXiv:1104.2549] [INSPIRE].ADSCrossRefGoogle Scholar - [67]J.R. Ellis, K.A. Olive and C. Savage,
*Hadronic uncertainties in the elastic scattering of supersymmetric dark matter*,*Phys. Rev.***D 77**(2008) 065026 [arXiv:0801.3656] [INSPIRE].ADSGoogle Scholar - [68]H. Ohki et al.,
*Nucleon sigma term and strange quark content from lattice QCD with exact chiral symmetry*,*Phys. Rev.***D 78**(2008) 054502 [arXiv:0806.4744] [INSPIRE].ADSGoogle Scholar - [69]J. Cao, K.-i. Hikasa, W. Wang, J.M. Yang and L.-X. Yu,
*Constraints of dark matter direct detection experiments on the MSSM and implications on LHC Higgs search*,*Phys. Rev.***D 82**(2010) 051701 [arXiv:1006.4811] [INSPIRE]. - [70]J. Alarcon, J. Martin Camalich and J. Oller,
*The chiral representation of the πN scattering amplitude and the pion-nucleon sigma term*,*Phys. Rev.***D 85**(2012) 051503 [arXiv:1110.3797] [INSPIRE].ADSGoogle Scholar - [71]D. Das, A. Goudelis and Y. Mambrini,
*Exploring SUSY light Higgs boson scenarios via dark matter experiments*,*JCAP***12**(2010) 018 [arXiv:1007.4812] [INSPIRE].ADSCrossRefGoogle Scholar - [72]ETM collaboration, S. Dinter et al.,
*Sigma terms and strangeness content of the nucleon with N*_{f}= 2 + 1 + 1*twisted mass fermions*,*JHEP***08**(2012) 037 [arXiv:1202.1480] [INSPIRE].ADSCrossRefGoogle Scholar - [73]Tevatron Electroweak Working Group, CDF, D0 collaboration,
*Combination of CDF and D0 results on the mass of the top quark using up to*5*.*8*fb*^{−1}*of data*, arXiv:1107.5255 [INSPIRE]. - [74]D. Eriksson, J. Rathsman and O. Stal,
*2HDMC: two-Higgs-doublet model calculator physics and manual*,*Comput. Phys. Commun.***181**(2010) 189 [arXiv:0902.0851] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar - [75]D. Eriksson, J. Rathsman and O. Stal,
*2HDMC: two-Higgs-doublet model calculator*,*Comput. Phys. Commun.***181**(2010) 833 [INSPIRE].ADSCrossRefGoogle Scholar - [76]S. Nie and M. Sher,
*Vacuum stability bounds in the two Higgs doublet model*,*Phys. Lett.***B 449**(1999) 89 [hep-ph/9811234] [INSPIRE].ADSCrossRefGoogle Scholar - [77]S. Kanemura, T. Kasai and Y. Okada,
*Mass bounds of the lightest CP even Higgs boson in the two Higgs doublet model*,*Phys. Lett.***B 471**(1999) 182 [hep-ph/9903289] [INSPIRE].ADSCrossRefGoogle Scholar - [78]Planck collaboration, P. Ade et al.,
*Planck 2013 results. XVI. Cosmological parameters*, arXiv:1303.5076 [INSPIRE]. - [79]P. Ferreira, R. Santos, M. Sher and J.P. Silva,
*Implications of the LHC two-photon signal for two-Higgs-doublet models*,*Phys. Rev.***D 85**(2012) 077703 [arXiv:1112.3277] [INSPIRE].ADSGoogle Scholar - [80]P. Ferreira, R. Santos, M. Sher and J.P. Silva,
*Could the LHC two-photon signal correspond to the heavier scalar in two-Higgs-doublet models?*,*Phys. Rev.***D 85**(2012) 035020 [arXiv:1201.0019] [INSPIRE].ADSGoogle Scholar - [81]A. Arhrib, R. Benbrik and N. Gaur,
*H*→*γγ in inert Higgs doublet model*,*Phys. Rev.***D 85**(2012) 095021 [arXiv:1201.2644] [INSPIRE].ADSGoogle Scholar - [82]W. Altmannshofer, S. Gori and G.D. Kribs,
*A minimal flavor violating 2HDM at the LHC*,*Phys. Rev.***D 86**(2012) 115009 [arXiv:1210.2465] [INSPIRE].ADSGoogle Scholar - [83]B. Swiezewska and M. Krawczyk,
*Diphoton rate in the inert doublet model with a*125*GeV Higgs boson*, arXiv:1212.4100 [INSPIRE]. - [84]F. Mahmoudi and O. Stal,
*Flavor constraints on the two-Higgs-doublet model with general Yukawa couplings*,*Phys. Rev.***D 81**(2010) 035016 [arXiv:0907.1791] [INSPIRE].ADSGoogle Scholar - [85]ATLAS collaboration,
*Search for charged Higgs bosons decaying via H*^{+}→*τν in top quark pair events using pp collision data at*\( \sqrt{s}=7 \)*TeV with the ATLAS detector*,*JHEP***06**(2012) 039 [arXiv:1204.2760] [INSPIRE].ADSGoogle Scholar - [86]CMS collaboration,
*Search for a light charged Higgs boson in top quark decays in pp collisions at*\( \sqrt{s}=7 \)*TeV*,*JHEP***07**(2012) 143 [arXiv:1205.5736] [INSPIRE].ADSGoogle Scholar - [87]ATLAS collaboration,
*Search for invisible decays of a Higgs boson produced in association with a Z boson in ATLAS*, ATLAS-CONF-2013-011 (2013). - [88]ATLAS collaboration,
*Measurements of the properties of the Higgs-like boson in the two photon decay channel with the ATLAS detector using*25*fb*^{−1}*of proton-proton collision data*, ATLAS-CONF-2013-012 (2013). - [89]CMS collaboration,
*Updated measurements of the Higgs boson at*125*GeV in the two photon decay channel*, CMS-PAS-HIG-13-001 (2013).