Closing in on singlet scalar dark matter: LUX, invisible Higgs decays and gamma-ray lines
CClosing in on singlet scalar dark matter: LUX,invisible Higgs decays and gamma-ray lines
Lei Feng, a Stefano Profumo, b Lorenzo Ubaldi c a Key Laboratory of Dark Matter and Space Astronomy,Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210008, China b Department of Physics and Santa Cruz Institute for Particle PhysicsUniversity of California, Santa Cruz, CA 95064, USA c Raymond and Beverly Sackler School of Physics and Astronomy,Tel-Aviv University, Tel-Aviv 69978, Israel
E-mail: [email protected] , [email protected] , [email protected] Abstract:
We study the implications of the Higgs discovery and of recent results fromdark matter searches on real singlet scalar dark matter. The phenomenology of the modelis defined by only two parameters, the singlet scalar mass m S and the quartic coupling a between the SU(2) Higgs and the singlet scalar. We concentrate on the window 5 0) with h real, the scalar potential reads V ( h, S ) = − µ λ − µ h + λvh + λ h + 12 ( b + a v ) S + b S + a vS h + a S h , (2.2)– 2 – ermiInvisibleHiggsdecays LUX 2015 Ω S > Ω DM �� ��� ��� ��� ��� ����� - � �� - � �� - � �� � �� � � � [ ��� ] � � Figure 1 . Along the cyan line the real scalar singlet gives the correct dark matter relic abundance.The region below this line corresponds to overabundance and is excluded, while most of the regionabove is excluded by experimental constraints. The strongest limits are from direct detection(LUX [43]): they exclude the region above the black line. Going to masses below a few GeVthe most important constraint comes from invisible Higgs decays searches [40], which exclude theregion above the purple line. We show several lines for the constraints from gamma-ray line searches(Fermi [38]): the plain lines correspond to the annihilation SS → γγ , the dashed lines to SS → γZ .The colors correspond to different dark matter density profiles: red is for Einasto, blue for NFW,green for Isothermal. Fermi excludes the area above these lines. The only regions which are notyet excluded are the white areas, one for m S > 110 GeV, the other on the lower left part of theplot, close to the resonance m S = m h / 2. We zoom into the resonant region in Fig. 2. where µ < λ is the quartic coupling for the Higgs, and ( − µ /λ ) / = v . This potentialis bounded from below, at tree level, provided that λ, b ≥ 0, and λb ≥ a for negative a .The singlet mass is, at tree level, m S = b + a v . (2.3)The phenomenology of this model is completely determined by the parameters a and b (or m S ), since the self-interaction quartic coupling b does not play any phenomenologicallyobservable role (see e.g. [26, 39]).In this paper we study experimental bounds on the two-dimensional parameter space { a , m S } and we update the results of our previous work [26]. Since then, the Higgs hasbeen discovered [35, 36], thus its mass is no longer a free parameter. In addition, we alsonow have constraints on the invisible Higgs decay h → SS [40–42], and both direct [37, 43]and indirect [38] detection limits have improved significantly.– 3 – Results Our results are summarized in Fig. 1. The cyan line in the plot represents the regionof parameter space where we obtain the correct dark matter relic abundance for S . Tocompute the relic density we solve numerically the Boltzmann equation d Y d x = Z ( x ) (cid:2) Y ( x ) − Y ( x ) (cid:3) , (3.1)where Y ≡ n/s , with n the number density of the scalar S , s the entropy density, x ≡ m S /T , Z ( x ) = (cid:114) π m S M Pl x [ √ g ∗ (cid:104) σv rel (cid:105) ]( x ) , (3.2) Y eq ( x ) = 454 π x h eff ( x ) K ( x ) , (3.3) √ g ∗ = h eff √ g eff (cid:18) T h eff d h eff d T (cid:19) . (3.4)Here T is the temperature, M Pl the reduced Planck mass, h eff and g eff the effective entropyand energy degrees of freedom, computed assuming SM particle content, K ( x ) a modifiedBessel function of the second kind. Eq. (3.1) is the usual Boltzmann equation that one hasto solve in order to find the relic density of a WIMP. Particular attention has to be paidto the thermal averaged annihilation cross section, especially in the resonant region. Wefollow the prescription of Ref. [44] (cid:104) σv rel (cid:105) = (cid:90) ∞ m S s (cid:113) s − m S K ( √ s/T ) σv rel T m S K ( m S /T ) d s . (3.5)Here K ( √ s/T ) is a modified Bessel function of the second kind, and s is the square of thecenter-of-mass energy. The details of the calculation of σv rel , which appears in the integralof eq. (3.5), are in Appendix A.Most of the region in which S would give the observed dark matter abundance isruled out by LUX [37, 43]. The direct detection constraint is obtained by comparing thespin-independent cross section for the scattering of S off of a nucleon, σ SI = a m N f πm S m h , (3.6)to the limits on σ SI provided by LUX. Here m N is the nucleon mass, and f is the form factorthat we take to be 1/3 [45, 46]. For values of m S larger than m h / σ , that enters the relic density calculation [see eq. (3.2)], and the directdetection cross section σ SI scale as a m S . However σ is constant, with (cid:104) σv rel (cid:105) ∼ × − cm s − , while the direct detection constraint on σ SI gets weaker at high masses as thenumber density of DM scales as 1 /m S . That is why for m S > 110 GeV the LUX constraintbecomes too weak to exclude S as a dark matter candidate. Other studies [10, 25] found We follow here the notation of Ref. [10]. – 4 – (cid:2)(cid:3)(cid:4)(cid:5)(cid:6)(cid:7)(cid:8)(cid:9) Ferminotexcluded (cid:1) (cid:2) (cid:3) (cid:4) (cid:5) (cid:6) (cid:7) (cid:8)(cid:2)(cid:1) - (cid:1) (cid:2)(cid:1) - (cid:2) (cid:2)(cid:1) - (cid:3) (cid:2)(cid:1) - (cid:4) (cid:2)(cid:1) - (cid:5) - (cid:9)(cid:10)(cid:11) (cid:6)(cid:7) [- (cid:1) ] (cid:1) (cid:5) - (cid:7) - (cid:6) - (cid:5) - (cid:4) - (cid:3) - (cid:2) (cid:1)(cid:2)(cid:1) - (cid:1) (cid:2)(cid:1) - (cid:2) (cid:2)(cid:1) - (cid:3) (cid:2)(cid:1) - (cid:4) (cid:2)(cid:1) - (cid:5) - (cid:9)(cid:10)(cid:11) (cid:6)(cid:7) [- (cid:1) ] (cid:1) (cid:5) Figure 2 . We use the same lines and color code as in the previous figure, but we trade the mass m S for the dimensionless parameter ∆ ≡ m S − m h m h in the horizontal axis, in order to zoom into theresonant region. Here the Fermi constraints are more severe than the ones from LUX (black line).The only region that escapes all current experimental constraints is for − − . < ∆ < − − . ,which corresponds to the mass range 54.9 GeV < m S < a similar allowed window. The only hope to close the available high-mass window is withbetter sensitivity of future direct detection experiments.At small values of m S the constraint from invisible Higgs decays becomes important.We utilize here the results of a recent study [40] according to which the branching fractionof the Higgs boson to invisible particles, in our case h → SS , has to be less than 0.40 at95% confidence level.The only limited region that escapes the above mentioned constraints is around m S (cid:39) m h / 2, where m h indicates the Higgs mass, a region we refer to as the “ resonant ” region.In the resonant region the constraints from gamma-ray-line searches by Fermi [38] areincreasingly important. We indicate different Fermi constraints with different line codingin the figures. The plain lines correspond to the SS → γγ channel, while the dashed linesto the SS → γZ channel. We use different colors for different choices of the Galactic DMdensity profile: red is for Einasto, blue for NFW, green for the Isothermal profile.Such constraints can be better appreciated by defining a new variable∆ ≡ m S − m h m h . (3.7)In Fig. 2 we employ the variable ∆ to show that the only region of the parameter space inwhich S is still a viable dark matter candidate is given by the range − − . < ∆ < − − . ,which corresponds to the mass range 54.9 GeV < m S < m S = m h / 2, and the reason is simple: In the early universe, attemperatures close to the freeze-out, we cannot simply use the approximation that S is non-relativistic, rather we should use eq. (3.5) to compute the thermal averaged cross section,which is valid in all regimes. The kinetic energy of the particles S ’s at that epoch, despitesmall, is non negligible and as a result the resonant condition in the annihilation, s = m h ,is met for values of m S smaller than m h / 2. On the other hand, when we compute theFermi constraints we are considering annihilations occurring in the Galactic center today,– 5 –n which case the temperature is much lower compared to the freeze-out temperature, thenon-relativistic approximation is perfectly fine and the resonant condition is m S (cid:39) m h / ρ singlet = ρ DM (Ω singlet / Ω DM ) . (3.8)Such a rescaling would have significantly weakened both direct and indirect detection limitsin the under-abundant regions. The rescaling is unnecessary on the cyan region indicatingΩ singlet = Ω DM . This is the region that provides the maximal ranges for the two keyparameters of the model, the mixing constant a and the singlet mass m S Fig. 2 elucidates the two key conclusions of our study:(1) below the resonance, the singlet scalar DM model is only viable for singlet scalarmasses in a narrow range, between 55 and 63 GeV, right below half the measuredSU(2) Higgs mass, by direct detection from below and by indirect detection fromabove, and(2) the allowed range for the singlet-SU(2) mixing constant a is constrained to betweenroughly 2 × − (cid:46) a (cid:46) × − , by the relic density over-production constraintfrom below, and by direction detection from above. We have reassessed the real singlet scalar extension to the SM as a possible context for theexplanation of the cosmological non-baryonic dark matter in light of the Higgs discovery andof improved direct and indirect dark matter detection constraints. We have demonstratedthat two small regions of parameter space remain viable: (i) within the small mass range55 (cid:46) m S / GeV (cid:46) 63 and for a similarly highly constrained range for the quartic coupling a between the singlet and the SU(2) Higgs; (ii) for m S > 110 GeV and a small range of a . A factor 20 improvement to the direct detection sensivity will conclusively test thismodel for m S below a TeV. Such an improvement is well within the reach of the plannedG2 direct detection experiments SuperCDMS and LZ [47]. New limits from Fermi-LAT willalso shrink the available parameter space, especially in the high-mass end of the currentlyopen parameter space near the resonance. The high mass ( m S > 110 GeV) region is alsostill viable, albeit for a very small range of a , and can be further constrained essentiallyonly with future direct detection experiments.The singlet, real scalar dark matter model is a clear example of how minimal setupsquickly become highly constrained, and thus highly predictive, with increasing quality of– 6 –xperimental data. Also, this specific context illustrates very clearly the complementarityacross a variety of different dark matter detection strategies, including direct, indirect andcollider searches. It will soon become clear whether or not this specific minimal extensionto the Standard Model of particle physics is or not the culprit for the fundamental natureof dark matter. Acknowledgments We thank Alessandro Strumia for a constructive discussion about the high-mass region ofthis model. We are grateful to Nicolas Bernal and James Cline for useful discussions. LFwas supported by 973 Program of China under grant 2013CB837000 and National NaturalScience of China under grant 11303096. SP is partly supported by the US Department ofEnergy, Contract DE-SC0010107-001. A Annihilation cross sections In this appendix we give explicit expressions for the cross sections relevant to the compu-tation of the relic density and of the gamma-ray line constraints. The annihilation of SS into any two-body final state XX , where XX is either a pair of fermions or a pair of gaugebosons, proceeds via the exchange of a Higgs boson in the s -channel. The cross sectiontimes the relative velocity of the annihilating particles is( σv rel ) XX = 8 a v √ s | D h ( s ) | Γ h → XX ( s ) , (A.1)where | D h ( s ) | ≡ s − m h ) + m h Γ h ( m h ) . (A.2)The width in the above propagator isΓ h ( m h ) = Γ vis + Γ inv , (A.3)Γ vis = 4 . 07 MeV , (A.4)Γ inv = a v πm h Re (cid:115) − m S m h , (A.5)while each of the widths Γ h → XX ( s ) in eq. (A.1) is obtained from the decay width of anoff-shell Higgs into the XX channel [48] substituting ( m ∗ h ) with s . In the computation ofthe relic density we take into account all the possible SM two-body final states, includingthe SS → hh channel for which we adopt the same cross section as in Ref. [10]:( σv rel ) hh = a πs V S (cid:20) ( a R + a I ) sV S V h + 8 a v (cid:18) a R − a v s − m h (cid:19) log (cid:12)(cid:12)(cid:12)(cid:12) m S − t + m S − t − (cid:12)(cid:12)(cid:12)(cid:12) + 8 a v sV S V h ( m S − t − )( m S − t + ) (cid:21) , (A.6)– 7 –here V i = (cid:113) − m i s , t ± = m S + m h − s (1 ∓ V S V h ), and a R ≡ m h ( s − m h ) | D h ( s ) | , (A.7) a I ≡ m h √ s Γ h ( m h ) | D h ( s ) | . (A.8)To apply the gamma-ray line constraints we are interested in the γγ and γZ channels.The corresponding widths are computed at one loop and are given by [49, 50]Γ h → γγ ( s ) = α s / π v (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:88) i N ci e i F i (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) , (A.9)Γ h → γZ ( s ) = αm W s / π v (cid:18) − m Z s (cid:19) (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:88) f N cf e f v f c W A Hf ( τ f , λ f ) + A HW ( τ W , λ W ) (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) . (A.10)Here α is the electromagnetic fine structure constant, c W and s W are respectively the cosineand sine of the Weinberg angle, the index i = f, W identifies whether the particle runningin the loop is a fermion or a W boson, N ci is its color multiplicity, e i its electric charge inunits of e , τ i = 4 m i /s and λ i = 4 m i /m Z , F f = − τ f [1 + (1 − τ f ) f ( τ f )] ,F W = 2 + 3 τ W + 3 τ W (2 − τ W ) f ( τ W ) , (A.11) f ( τ ) = (cid:104) sin − ( (cid:112) /τ ) (cid:105) , if τ ≥ − (cid:104) ln (cid:16) √ − τ −√ − τ (cid:17) − iπ (cid:105) , if τ < v f = 2 I f − e f s W , with I f the fermion weak isospin, A Hf = [ I ( τ, λ ) − I ( τ, λ )] (A.13) A HW ( τ, λ ) = c W (cid:26) (cid:18) − s W c W (cid:19) I ( τ, λ ) + (cid:20)(cid:18) τ (cid:19) s W c W − (cid:18) τ (cid:19)(cid:21) I ( τ, λ ) (cid:27) , (A.14)the functions I and I are given by I ( τ, λ ) = τ λ τ − λ ) + τ λ τ − λ ) [ f ( τ ) − f ( λ )] + τ λ ( τ − λ ) [ g ( τ ) − g ( λ )] , (A.15) I ( τ, λ ) = − τ λ τ − λ ) [ f ( τ ) − f ( λ )] , (A.16)with g ( τ ) = (cid:40) √ τ − − ( (cid:112) /τ ) , if τ ≥ √ − τ (cid:104) ln (cid:16) √ − τ −√ − τ (cid:17) − iπ (cid:105) , if τ < . (A.17)– 8 – Note on the Fermi constraints In the model we are considering there are two annihilation processes that can give rise togamma-ray lines. One is SS → γγ , the other SS → γZ . The corresponding cross sectionsare given in Appendix A. The Fermi collaboration provides limits [38] on the flux, Φ γ , ofgamma rays from dark matter annihilation for photon energies between 5 and 300 GeV.They also translate the limits on the flux directly into limits on the annihilation crosssection to γγ , thus comparing the cross section in our model for that channel to thoseconstraints is straightforward. They leave to us the simple exercise of translating the fluxlimits into limits on the annihilation cross section to γZ . The exercise is done as follows.In the process SS → γZ , the energy of the monochromatic photon is E γ = m S (cid:18) − m Z m S (cid:19) . (B.1)As the range of the Fermi search starts at E γ = 5 GeV, this implies that the minimummass probed in this channel is m S (cid:39) 48 GeV, as it is reflected in the plot of Fig. 1. Theflux is given by Φ γ = (cid:104) σv rel (cid:105) γZ πm S J ann , (B.2)where the J-factor, J ann , is the integral of ρ ( r ) along the line of sight, with ρ ( r ) the darkmatter density profile. The J-factors corresponding to four different dark matter profilesare listed in Table III of Ref. [38]. Combining eqs. (B.1) and (B.2) we get (cid:104) σv rel (cid:105) γZ = 1 J ann π (cid:16) E γ + (cid:113) E γ + m Z (cid:17) Φ γ . (B.3)Then from the upper limits on Φ γ listed in Table VII of Ref. [38], we can set constraintson (cid:104) σv rel (cid:105) γZ . References [1] M. Veltman and F. Yndurain, Radiative corrections to WW scattering , Nucl.Phys. B325 (1989) 1.[2] V. Silveira and A. Zee, Scalar Phantoms , Phys.Lett. B161 (1985) 136.[3] J. McDonald, Gauge singlet scalars as cold dark matter , Phys.Rev. D50 (1994) 3637–3649,[ hep-ph/0702143 ].[4] C. Burgess, M. Pospelov, and T. ter Veldhuis, The Minimal model of nonbaryonic darkmatter: A Singlet scalar , Nucl.Phys. B619 (2001) 709–728, [ hep-ph/0011335 ].[5] V. Barger, P. Langacker, M. McCaskey, M. J. Ramsey-Musolf, and G. Shaughnessy, LHCPhenomenology of an Extended Standard Model with a Real Scalar Singlet , Phys.Rev. D77 (2008) 035005, [ arXiv:0706.4311 ].[6] P. H. Damgaard, D. O’Connell, T. C. Petersen, and A. Tranberg, Constraints on NewPhysics from Baryogenesis and Large Hadron Collider Data , Phys.Rev.Lett. (2013),no. 22 221804, [ arXiv:1305.4362 ]. – 9 – 7] J. M. No and M. Ramsey-Musolf, Probing the Higgs Portal at the LHC Through Resonantdi-Higgs Production , Phys.Rev. D89 (2014) 095031, [ arXiv:1310.6035 ].[8] X.-G. He, T. Li, X.-Q. Li, J. Tandean, and H.-C. Tsai, The Simplest Dark-Matter Model,CDMS II Results, and Higgs Detection at LHC , Phys.Lett. B688 (2010) 332–336,[ arXiv:0912.4722 ].[9] M. Gonderinger, Y. Li, H. Patel, and M. J. Ramsey-Musolf, Vacuum Stability,Perturbativity, and Scalar Singlet Dark Matter , JHEP (2010) 053, [ arXiv:0910.3167 ].[10] J. M. Cline, K. Kainulainen, P. Scott, and C. Weniger, Update on scalar singlet dark matter , Phys.Rev. D88 (2013) 055025, [ arXiv:1306.4710 ].[11] K. Petraki and A. Kusenko, Dark-matter sterile neutrinos in models with a gauge singlet inthe Higgs sector , Phys.Rev. D77 (2008) 065014, [ arXiv:0711.4646 ].[12] F. S. Queiroz and K. Sinha, The Poker Face of the Majoron Dark Matter Model: LUX tokeV Line , Phys.Lett. B735 (2014) 69–74, [ arXiv:1404.1400 ].[13] A. Drozd, B. Grzadkowski, and J. Wudka, Multi-Scalar-Singlet Extension of the StandardModel - the Case for Dark Matter and an Invisible Higgs Boson , JHEP (2012) 006,[ arXiv:1112.2582 ].[14] A. Djouadi, O. Lebedev, Y. Mambrini, and J. Quevillon, Implications of LHC searches forHiggs–portal dark matter , Phys.Lett. B709 (2012) 65–69, [ arXiv:1112.3299 ].[15] A. Djouadi, A. Falkowski, Y. Mambrini, and J. Quevillon, Direct Detection of Higgs-PortalDark Matter at the LHC , Eur.Phys.J. C73 (2013), no. 6 2455, [ arXiv:1205.3169 ].[16] M. Raidal and A. Strumia, Hints for a non-standard Higgs boson from the LHC , Phys.Rev. D84 (2011) 077701, [ arXiv:1108.4903 ].[17] S. Baek, P. Ko, and W.-I. Park, Local Z scalar dark matter model confronting galactic G eV -scale γ -ray and muon ( g − arXiv:1407.6588 .[18] S. Baek, P. Ko, and W.-I. Park, Invisible Higgs Decay Width vs. Dark Matter DirectDetection Cross Section in Higgs Portal Dark Matter Models , Phys.Rev. D90 (2014), no. 5055014, [ arXiv:1405.3530 ].[19] P. Ko, W.-I. Park, and Y. Tang, Higgs portal vector dark matter for GeV scale γ -ray excessfrom galactic center , JCAP (2014) 013, [ arXiv:1404.5257 ].[20] D. Stojkovic, Implications of the Higgs discovery for gravity and cosmology , Int.J.Mod.Phys. D22 (2013) 1342017, [ arXiv:1305.6960 ].[21] T. Robens and T. Stefaniak, Status of the Higgs Singlet Extension of the Standard Modelafter LHC Run 1 , arXiv:1501.0223 .[22] K. Cheung, Y.-L. S. Tsai, P.-Y. Tseng, T.-C. Yuan, and A. Zee, Global Study of the SimplestScalar Phantom Dark Matter Model , JCAP (2012) 042, [ arXiv:1207.4930 ].[23] C. E. Yaguna, The Singlet Scalar as FIMP Dark Matter , JHEP (2011) 060,[ arXiv:1105.1654 ].[24] A. Goudelis, Y. Mambrini, and C. Yaguna, Antimatter signals of singlet scalar dark matter , JCAP (2009) 008, [ arXiv:0909.2799 ].[25] A. De Simone, G. F. Giudice, and A. Strumia, Benchmarks for Dark Matter Searches at theLHC , JHEP (2014) 081, [ arXiv:1402.6287 ]. – 10 – 26] S. Profumo, L. Ubaldi, and C. Wainwright, Singlet Scalar Dark Matter: monochromaticgamma rays and metastable vacua , Phys.Rev. D82 (2010) 123514, [ arXiv:1009.5377 ].[27] M. Kadastik, K. Kannike, A. Racioppi, and M. Raidal, Implications of the 125 GeV Higgsboson for scalar dark matter and for the CMSSM phenomenology , JHEP (2012) 061,[ arXiv:1112.3647 ].[28] J. Espinosa and M. Quiros, The Electroweak phase transition with a singlet , Phys.Lett. B305 (1993) 98–105, [ hep-ph/9301285 ].[29] A. Noble and M. Perelstein, Higgs self-coupling as a probe of electroweak phase transition , Phys.Rev. D78 (2008) 063518, [ arXiv:0711.3018 ].[30] J. M. Cline, G. Laporte, H. Yamashita, and S. Kraml, Electroweak Phase Transition andLHC Signatures in the Singlet Majoron Model , JHEP (2009) 040, [ arXiv:0905.2559 ].[31] J. M. Cline and K. Kainulainen, Electroweak baryogenesis and dark matter from a singletHiggs , JCAP (2013) 012, [ arXiv:1210.4196 ].[32] A. Katz and M. Perelstein, Higgs Couplings and Electroweak Phase Transition , JHEP (2014) 108, [ arXiv:1401.1827 ].[33] K. Fuyuto and E. Senaha, Improved sphaleron decoupling condition and the Higgs couplingconstants in the real singlet-extended SM , Phys.Rev. D90 (2014) 015015, [ arXiv:1406.0433 ].[34] S. Profumo, M. J. Ramsey-Musolf, C. L. Wainwright, and P. Winslow, Singlet-CatalyzedElectroweak Phase Transitions and Precision Higgs Studies , arXiv:1407.5342 .[35] CMS Collaboration Collaboration, S. Chatrchyan et al., Observation of a new boson at amass of 125 GeV with the CMS experiment at the LHC , Phys.Lett. B716 (2012) 30–61,[ arXiv:1207.7235 ].[36] ATLAS Collaboration Collaboration, G. Aad et al., Observation of a new particle in thesearch for the Standard Model Higgs boson with the ATLAS detector at the LHC , Phys.Lett. B716 (2012) 1–29, [ arXiv:1207.7214 ].[37] LUX Collaboration Collaboration, D. Akerib et al., First results from the LUX darkmatter experiment at the Sanford Underground Research Facility , Phys.Rev.Lett. (2014)091303, [ arXiv:1310.8214 ].[38] Fermi-LAT Collaboration Collaboration, M. Ackermann et al., Search for Gamma-raySpectral Lines with the Fermi Large Area Telescope and Dark Matter Implications , Phys.Rev. D88 (2013) 082002, [ arXiv:1305.5597 ].[39] S. Profumo, M. J. Ramsey-Musolf, and G. Shaughnessy, Singlet Higgs phenomenology andthe electroweak phase transition , JHEP (2007) 010, [ arXiv:0705.2425 ].[40] N. Zhou, Z. Khechadoorian, D. Whiteson, and T. M. Tait, Bounds on Invisible Higgs bosonDecays from t ¯ tH Production , arXiv:1408.0011 .[41] ATLAS Collaboration Collaboration, G. Aad et al., Search for Invisible Decays of a HiggsBoson Produced in Association with a Z Boson in ATLAS , Phys.Rev.Lett. (2014)201802, [ arXiv:1402.3244 ].[42] CMS Collaboration Collaboration, S. Chatrchyan et al., Search for invisible decays ofHiggs bosons in the vector boson fusion and associated ZH production modes , Eur.Phys.J. C74 (2014) 2980, [ arXiv:1404.1344 ]. – 11 – LUX Collaboration, D. S. Akerib et al., Improved WIMP scattering limits from the LUXexperiment , arXiv:1512.0350 .[44] P. Gondolo and G. Gelmini, Cosmic abundances of stable particles: Improved analysis , Nucl.Phys. B360 (1991) 145–179.[45] M. Farina, D. Pappadopulo, and A. Strumia, CDMS stands for Constrained Dark MatterSinglet , Phys.Lett. B688 (2010) 329–331, [ arXiv:0912.5038 ].[46] J. Giedt, A. W. Thomas, and R. D. Young, Dark matter, the CMSSM and lattice QCD , Phys.Rev.Lett. (2009) 201802, [ arXiv:0907.4177 ].[47] P. Cushman, C. Galbiati, D. McKinsey, H. Robertson, T. Tait, et al., Working GroupReport: WIMP Dark Matter Direct Detection , arXiv:1310.8327 .[48] LHC Higgs Cross Section Working Group Collaboration, S. Dittmaier et al., Handbookof LHC Higgs Cross Sections: 1. Inclusive Observables , arXiv:1101.0593 .[49] J. F. Gunion, H. E. Haber, G. L. Kane, and S. Dawson, The Higgs Hunter’s Guide , Front.Phys. (2000) 1–448.[50] A. Djouadi, The Anatomy of electro-weak symmetry breaking. I: The Higgs boson in thestandard model , Phys.Rept. (2008) 1–216, [ hep-ph/0503172 ].].