An Updated Analysis of Inert Higgs Doublet Model in light of the Recent Results from LUX, PLANCK, AMS-02 and LHC

In light of the recent discovery by the ATLAS and CMS experiments at the Large Hadron Collider (LHC) of a Higgs-like particle with a narrow mass range of 125-126 GeV, we perform an updated analysis on one of the popular scalar dark matter models, the Inert Higgs Doublet Model (IHDM). We take into account in our likelihood analysis of various experimental constraints, including recent relic density measurement, dark matter direct and indirect detection constraints as well as the latest collider constraints on the invisible decay width of the Higgs boson and monojet search at the LHC. It is shown that if the invisible decay of the standard model Higgs boson is open, LHC as well as direct detection experiments like LUX and XENON100 could put stringent limits on the Higgs boson couplings to dark matter. We find that the most favoured parameter space for IHDM corresponds to dark matter with a mass less than 100 GeV or so. In particular, the best-fit points are at the dark matter mass around 70 GeV where the invisible Higgs decay to dark matter is closed. Scalar dark matter in the higher mass range of 0.5-4 TeV is also explored in our study. Projected sensitivities for the future experiments of monojet at LHC-14, XENON1T and AMS-02 one year antiproton flux are shown to put further constraints on the existing parameter space of IHDM.


Abstract
In light of the recent discovery by the ATLAS and CMS experiments at the Large Hadron Collider (LHC) of a Higgs-like particle with a narrow mass range of 125-126 GeV, we perform an updated analysis on one of the popular scalar dark matter models, the Inert Higgs Doublet Model (IHDM).
We take into account in our likelihood analysis of various experimental constraints, including recent relic density measurement, dark matter direct and indirect detection constraints as well as the latest collider constraints on the invisible decay width of the Higgs boson and monojet search at the LHC. It is shown that if the invisible decay of the standard model Higgs boson is open, LHC as well as direct detection experiments like LUX and XENON100 could put stringent limits on the Higgs boson couplings to dark matter. We find that the most favoured parameter space for IHDM corresponds to dark matter with a mass less than 100 GeV or so. In particular, the best-fit points are at the dark matter mass around 70 GeV where the invisible Higgs decay to dark matter is closed. Scalar dark matter in the higher mass range of 0.5-4 TeV is also explored in our study.

I. INTRODUCTION
The 7 TeV and 8 TeV run at the Large Hadron Collider (LHC) have revealed and confirmed the existence of a Higgs-like particle h in the standard model (SM) with mass in the narrow range of 125-126 GeV [1,2]. This discovery is also verified by the recent Tevatron final results [3]. The observation of this new particle combines evidence in the decays h → γγ, h → ZZ * and h → W ± W ∓ * . Different signal strengths, defined as the product of Higgs boson production cross sections from different channels and the branching ratios for different decay modes normalized to the corresponding products in SM, have been measured with good precision by both experiments at ATLAS and CMS [4][5][6]. These measurements will be further improved in the future [13][14] TeV run at the LHC, and perhaps at a future International Linear Collider (ILC) should this machine ever be built. From these signal strengths measurement one can extract information on the couplings of this Higgs-like particle to the gauge bosons and SM fermions. From the most recent measurements, extraction of this Higgs-like particle couplings to SM particles seem to be consistent to a great extent with those of the SM Higgs boson couplings [7]. Moreover, data collected both at ATLAS and CMS indicate that this Higgs-like particle has zero spin and is CP-even, i.e. J P = 0 + is preferred [8,9].
The discovery of the Higgs-like particle at the LHC indicates for the first time that fundamental scalar exists in Nature. Certainly, many phenomenological models that extend the SM scalar sector with just one scalar doublet existed already in the literature. Some of them are motivated by physics of the dark matter (DM) or neutrinos masses. Among these extensions, we have models with multiple Higgs doublets, with one Higgs doublet and multiple singlets or triplets etc. All these extensions should have one light scalar with Higgs-like couplings to SM particles in the range tolerated by signal strength measurements. Indeed many studies (see for example the references in [7]) have been done using these data to constrain various extensions of the scalar sector of the SM.
In this paper, we concentrate on the Inert Higgs Doublet Model (IHDM) which is a very simple extension of the SM. It was first proposed by Deshpande and Ma [10] in order to study the pattern of electroweak symmetry breaking. The IHDM is an attractive model due to its simplicity. It is basically a Two Higgs Doublet Model (THDM) (see [11] for a recent overview) with an imposed exact Z 2 symmetry. Under the Z 2 symmetry, all the SM particles are even representing the visible sector, while the new Higgs doublet field is odd representing the inert dark sector. Imposing the Z 2 symmetry forbids the second Higgs doublet developing a vacuum expectation value (VEV) and all the inert particles in this doublet can only appear in pair in their interaction vertices. Indeed, recent studies [12][13][14][15] of global fits of the LHC data suggest that the couplings between the W and Z gauge bosons with the new 125-126 GeV Higgs-like boson are very close to their SM values. The new 125-126 GeV boson may play the entire role of electroweak symmetry breaking (EWSB) and leave no room for other Higgs fields to develop any VEVs. This favors the IHDM. As a result, IHDM exhibits very interesting phenomenology. It predicts the existence of a neutral scalar field, denoted generically by χ here, which is the Lightest Odd Particle (LOP) in this model and will play the role of DM candidate. The Higgs mechanism provides a portal for communication between the inert dark sector and the visible SM sector. Thus if kinematics allowed, the SM Higgs boson may decay into a pair of DM χ and will contribute to the invisible SM Higgs boson width which is now constrained by the LHC data. Moreover, annihilation of χ into SM particles will provide thermal relic density and the scattering of χ onto nucleons will lead to direct detection signatures. Therefore, IHDM could be considered as a simple but competitive model in the market with a weakly interacting massive particle (WIMP). As we will see later, IHDM could predict correct DM relic density as well as a cross section for scattering of χ onto nucleons that is consistent with existing data from direct detection. Almost three decades later, IHDM was extended further by Ma [16] to include three Z 2 odd weak singlets of right-handed neutrinos with Majorana masses. In this extended model [16], a radiative seesaw mechanism for light neutrino masses was proposed and either χ or one of the right-handed neutrinos could be DM candidate. We will not consider this extended version of IHDM in this work but would like to return to this in the future [17].
As mentioned earlier, there have been many attempts to introduce DM Higgs models by extending the SM scalar sector with more singlets or doublets [18][19][20][21][22]. In particular, the phenomenology of IHDM had been extensively discussed in the context of DM phenomenology [23][24][25][26][27][28] and also for collider phenomenology [29][30][31]. IHDM has been also advocated to explain the naturalness problem [32]. In the present study, we will reconsider the IHDM model in light of the recent ATLAS and CMS discovery of a Higgs-like particle of 125-126 GeV. We assume that the LOP must fulfill the recent relic density measurement by PLANCK [33].
As a good DM candidate test, we also consider the constraints from DM direct and indirect detection. For the constraint from DM direct detection search, we study the impact from the most recent LUX upper limit [34] which provides a robust constraint on the parameter space. As for indirect detection, we will take into account the Fermi-LAT γ-ray observations of the dwarf spheroidal galaxies (dSphs) [35] and the Galactic center (GC) [36]. In addition to γ-rays, we also include constraints from cosmic ray electrons/positrons from AMS-02 [37], PAMELA [38], and Fermi-LAT [39,40], and cosmic ray anti-protons from PAMELA [41].
These constraints will be also supplemented by the LHC constraints such as monojet and diphoton signal strength measurement as well as constraint on the Higgs boson invisible decay width. Some of the above aspects for IHDM have been discussed in recent studies [23,24].
The compatibility of a heavy SM Higgs boson with LHC results and XENON100 data [42] were discussed in Ref. [23] 1 . Similar issues for IHDM were discussed in Ref. [24] with the inclusion of radiative corrections to the scalar masses of the model. Ref. [24] also included renormalization group effects for the quartic scalar couplings λ i in order to evaluate vacuum stability, perturbativity and unitarity constraints at a higher scale. In our analysis, we will go further by including also the following aspects: 1. Larger parameter space for DM mass: we will scan m χ from 5 GeV to 4 TeV.
3. Accurate DM indirect detection likelihood. 4. Constraints from the first result of LUX in direct detection likelihood. 5. Future sensitivity to monojet search at LHC with 14 TeV at the planned luminosity of 100 fb −1 and 300 fb −1 .
The layout of this paper is as follows. In section 2, we briefly review IHDM and its parameterization. We then list the theoretical constraints such as perturbativity, perturbative 1 In a note added in [23], the consistency of IHDM with the 125-126 GeV Higgs-like particle observed at LHC and XENON100 were also discussed. unitarity and vacuum stability that must be satisfied by the scalar potential parameters.
The constraints from collider searches that IHDM is subjected to are discussed in section 3. These include: electroweak precision test constraints, W and Z width constraints, negative search for charginos and neutralinos from LEP-II that could restrict the inert Higgs bosons masses, diphoton signal strength measurement as well as monojet constraint from DM search at LHC. In section 4, we will discuss the relic density measurement by PLANCK as well as DM direct detection and indirect detection constraints. In section 5, we present our methodology for likelihood analysis and explain how all the constraints are included. We present our numerical results in section 6. Future experimental constraints from LHC-14, XENON1T and AMS-02 are discussed in section 7. We conclude in section 8.

II. INERT HIGGS DOUBLET MODEL (IHDM)
In this section, we briefly review the salient features of IHDM and discuss some existing theoretical constraints.
where G ± and G 0 are the charged and neutral Goldstone bosons respectively, which will be absorbed by the W ± and Z to acquire their masses.
The scalar potential with an exact Z 2 symmetry forbids the mass term −µ 2 12 (H † 1 H 2 +h.c.) which mixes H 1 and H 2 . Thus it has one fewer term than in THDM, i.e.
The above scalar potential in Eq.
(2) has 8 real parameters: 5 λ i , 2 µ 2 i and the VEV v. Minimization condition for the scalar potential eliminates µ 2 1 in favour of the Higgs mass and the VEV v is fixed to be 246 GeV by the weak gauge boson masses. We are left with 6 independent real parameters. The masses of all the four physical scalars can be written in terms of µ 2 2 , λ 1 , λ 2 , λ 3 , λ 4 and λ 5 as the following where Four of the five quartic couplings can be written in terms of physical scalar masses and µ 2 2 as the following expressions We are then free to take (λ i ) i=1,...,5 and µ 2 2 as 6 independent parameters, or equivalently, the following set which is more convenient for our purposes to describe the full scalar sector. In our tree level parameterization, λ A can be expressed as It is clear from Eq. (11) that λ A > λ L for m A > m S and λ A < λ L for m A < m S . In our systematic scan in the following numerical work, we will consider both cases where χ = S or χ = A being the LOP. Thus, the DM mass is defined as In order to illustrate constraint on λ L,A with S or A being the LOP, we define the coupling g hχχ as The coupling g hχχ shows up directly in the relic density computation depends on whether

B. Theoretical constraints
The parameters of the scalar potential of the IHDM are severely constrained by theoretical constraints. First, to trust our perturbative calculations we have to require all quartic couplings in the scalar potential of Eq. (2) to obey |λ i | ≤ 8π. Second, in order to have a scalar potential bounded from below we must also demand the following constraints [11]: Third, to further constrain the scalar potential parameters of the IHDM one can impose tree-level unitarity in a variety of scattering processes among the various scalars and gauge bosons. For the unitarity constraints, it is convenience to define the following twelve parameters e i [27]: 8 The perturbative unitarity constraints are then imposed on all e i satisfying [27] |e i | ≤ 8π , ∀ i = 1, ..., 12.

III. COLLIDER CONSTRAINTS
In this section, we discuss DM constraints from the collider search experiments. We will focus on the constraints from the electroweak precision test (EWPT) experiments at LEP-II, neutral and charged Higgs search at LEP-II, as well as the mass and the invisible width of the Higgs, diphoton signal strength and monojet search from the LHC.
• Electroweak precision tests: EWPT is a common approach to constrain physics beyond SM by using the global electroweak fit through the oblique S, T and U parameters [44]. It is well known that in the SM the EWPT implies a close relation between the three masses m t , m h and m W . Similarly, in the IHDM, the EWPT implies constraints on the mass splitting among the Higgs boson masses [32]. In this study, we will use the PDG values of S and T with U fixed to be zero [45]. We allow S and T parameters to be within 95% C.L. (Confidence Level). The central value of S and T , assuming a SM Higgs boson mass of m h = 126 GeV, are given by [45] : The correlation between S and T is 91% in this fit. Analytic expressions for S and T in IHDM can be found in Ref. [32].
• LEP limits on neutral and charged Higgs bosons: Other LEP constraints come from the precise measurements of W and Z widths. In order not to affect these decay widths we demand that the channels W ± → {SH ± , AH ± } In the IHDM, if S is the LOP the CP-odd A could decay like A → SZ, while the charged Higgs boson H ± could decay into W ± S and/or W ± A followed by A → SZ.
Therefore the final states of the two production processes e + e − → H + H − and e + e − → SA would be multi-leptons or multi-jets, depending on the decay products of W ± and Z, plus missing energies. To certain extents, the signatures for the charged Higgs case would be similar to the supersymmetry searches for charginos and neutralinos at e + e − or at hadron colliders [29,30]. 2 Taking into account these considerations, we will safely choose in our scan for the charged Higgs mass m H ± being always greater than 70 GeV. For the neutral inert Higgses S and A, neutralinos search at LEP-II via e + e − → χ 0 1 χ 0 2 followed by χ 0 2 → χ 0 1 ff [48] could apply here since the process e + e − → SA followed by the cascade A → SZ → Sff would give similar signals.
Such analysis had been carefully done in Ref. [31]. Their limits on m S and m A can be summarized as max(m A , m S ) ≥ 100 GeV. However, in the present study, we will use the exact exclusion region as given in Ref. [31].
• Higgs mass: In the IHDM, the SM Higgs boson h have similar couplings to SM fermions and gauge bosons. Therefore, as long as h decays into SM final states, all the measurements from ATLAS and CMS experiments about SM Higgs boson properties can be used.
In particular, we will require the mass of the SM Higgs boson of the IHDM should lie 2 The projection of the experimental limits from SUSY searches to IHDM has to be made with some care since the production cross sections for the fermionic chargino/neutralino pair in the SUSY case are different from the scalar pairs of H ± H ∓ and SH ± in the IHDM case [47]. The cross sections for fermionic and scalar pair production are scaled by β 1/2 and β 3/2 respectively, where β is the velocity of the final state particle in the center-of-mass frame. Hence, the scalar pair will be suppressed by an extra factor of β as compared with the fermionic case. within the measurement [6]: • Invisible decay: The openings of one of the non-standard decays of the Higgs boson such as h → SS This constraint on the invisible decay is rather weak compared to the one derived from various works of global fits to ATLAS and CMS data [12][13][14][15]. These global fits studies suggest that the branching ratio of the invisible decay of the Higgs boson should not exceed 19% at 95% C.L. in the case where the Higgs boson has SM-like couplings to all SM particles plus additional invisible decay mode which is exactly the case as in IHDM. On the other hand, if one allows for deviation in the hγγ (and hgg as well on general grounds but not for IHDM) coupling from its SM value the 95% C.L. limit on the invisible Higgs decay branching ratio moves up to 29% [14].
• Diphoton signal strength R γγ in the IHDM: Assuming that the production cross section of the Higgs boson is dominated by the gluon gluon fusion process, the diphoton signal strength in the IHDM normalized to the SM value can be simplified as where in the first line we have used the narrow width approximation and in the second line we used the fact that σ(gg → h) is the same in both the SM and IHDM. Thus the signal strength R γγ in IHDM is simply given by the ratio of the branching ratios, which is not necessarily one since the charged Higgs boson in IHDM can provide extra contribution other than the SM particles to the triangle loop amplitude of h → γγ.
At ATLAS, the overall signal strength for diphoton is about 1.55 +0.33 −0.28 , which corresponds to about 2σ deviation from the SM prediction [52], while the other channels are consistent with SM. However, at CMS, the new analysis for diphoton mode based on multivariate analysis [53] gives a signal strength about 0.78 ± 0.28, which is consistent with SM. Many proposals based on physics beyond SM, including IHDM, have been suggested to explain the diphoton excess, but the actual disagreement between ATLAS and CMS does not allow to draw any definite conclusions yet, given the current level of statistics. In the present analysis we will not try to explain the diphoton excess but rather study the impact of the other constraints on the ratio R γγ .
• LHC monojet search: Besides using the invisible width of the Higgs decay, another strategy to look for DM at the LHC is to study high p T monojet balanced by a large missing transverse energy E T [54, 55]. Such kind of signature is possible in IHDM by producing the SM Higgs boson h in association with an energetic jet followed by the invisible decay of h. In our analysis we will consider the following parton processes: gb → hb → χχ + b: s-channel and t-channel tree level diagrams with the Higgs boson radiated from b quark legs, -qg → hq → χχ + q: t-channel diagram through tree level gluon-quark-anti-quark vertex and one-loop hgg effective vertex, -gg → hg → χχ + g: t-channel diagram through tree level three gluon vertex and one-loop hgg effective vertex, -qq → hg → χχ + g: s-channel diagram through tree level gluon-quark-anti-quark vertex and one-loop hgg effective vertex.
In all these processes, the final state consists of a pair of invisible DM particles plus a quark or gluon jet. For the experimental cuts, see the later discussion of the likelihood function for the monojet data in section V.

CONSTRAINTS
It is well known that annihilation of χ into SM particles and other inert Higgs bosons can contribute to thermal relic density as well as indirect DM signals of high energy gamma-rays, positrons, antiprotons or neutrinos, while the scattering of χ onto nuclei will lead to direct detection signals by measuring the recoil energy of the nuclei via scintillation light, heat or ionization or some combinations of these three different signals using different technologies.
• Relic density constraint: Assuming a standard thermal evolution of our Universe, we compute the relic density from the following channels: χχ → ff (f = t, b, c, τ, µ), χχ → W ± W ∓ , ZZ, γγ, γZ and χχ → H ± H ∓ . Since χ can be either S or A, we consider SS or AA annihilation.
Note that in the case where m χ < m W,Z , we take into account the annihilation into 3-body final state from V V * or 4-body final state from V * V * (V = W ± , Z). All the annihilation into SM particles channels proceed through s-channel Higgs boson exchange while the annihilation into inert Higgs particles such as H ± H ∓ , hh and AA will proceed through both s-channel and t-channel Higgs boson exchange as well as the contact interactions with the quartic couplings for the χχH ± H ∓ , χχhh and χχAA/SS vertices. The calculation is done using the public code MicrOMEGAs [56].
The outcome of our relic density calculation should be in agreement with the recent PLANCK measurement [57]: As is well known if the mass splitting between the LOP and Next-Lightest Odd Particle (NLOP) is 10 GeV or so, the number densities of these NLOPs have only slight Boltzmann suppression with respect to the LOP number density. Therefore, the contributions to the relic density from the scattering of LOP-NLOP and NLOP-NLOP have to be taken into account in order to have a more precise relic density prediction.
These mechanisms are known as coannihilation [58,59]. As these are implemented already in the package MicrOMEGAs [56], we can take the S − A, S − H ± and A − H ± coannihilation into account at ease.
• The LUX limit: At present the most stringent limit on the spin-independent component of elastic scattering cross section σ SI p for χp → χp comes from LUX [34]. They improved the minimum σ SI p upper limit obtained by XENON100 [42] about an overall factor of 3. This result then sets the limit on the spin-independent cross section, σ SI p < 8 × 10 −10 pb for DM mass m χ ≈ 33 GeV. In this study, we include the 90% upper limit obtained in [34] for σ SI p versus the DM mass in our likelihood function. However, one should bear in mind that σ SI p may be susceptible to large theoretical uncertainties from the hadronic matrix elements. We will take into account the uncertainties in the hadronic matrix elements, as will be discussed later in section V.
• Gamma-rays: We consider the Fermi-LAT observations of γ-rays from dSphs [35,60,61] and GC [36]. The 10 dSphs as adopted in [35] will be used in this work. Four years of the Fermi-LAT data 4 , recorded from 4 August 2008 to 2 August 2012 with the pass 7 photon selection, are employed in this analysis. The energy range of photons is chosen from 200 MeV to 500 GeV, and the region-of-interest (ROI) is adopted to be a 14 • ×14 • box centered on each dSphs. For the GC analysis, a slightly smaller ROI region of 10 • ×10 • is chosen to avoid too many sources in the analysis. In the likelihood analysis, the normalization of the diffuse background models 5 gal 2yearp7v6 v0.fits and iso p7v6source.txt, and the point sources located in the ROIs in the second LAT catalog [62] are left free to do the minimization. The Fermi-LAT data are binned into 11 energy bins logarithmically spaced between 0.2 and 410 GeV, and we calculate 4 http://fermi.gsfc.nasa.gov/ssc/data 5 http://fermi.gsfc.nasa.gov/ssc/data/access/lat/BackgroundModels.html the likelihood map of Fermi-LAT dSphs and GC observations on the E bin −flux plane following the method developed in [61]. Such a method is very efficient to derive the final likelihood of any specific γ-ray spectrum, and is tested to be consistent with the standard analysis procedure using Fermi Scientific Tool [61].
• Cosmic ray electrons and positrons: The cosmic ray positron fraction measured by PAMELA [38] and most recently by AMS-02 [37] show clear evidence of excess compared with the secondary production as expected from the cosmic ray propagation model. The fluxes of the total e + e − measured by ATIC [63], Fermi-LAT [40], HESS [64] and MAGIC [65] also show the deviation from the extrapolation of the low energy PAMELA data [66], which further supports the existence of extra e + e − sources. There are many models proposed to account for the e + e − excesses, including the astrophysical sources such as pulsars and supernova remnants, and DM annihilation/decay (see e.g. the review articles [67]). While the DM model would suffer from strong constraints from γ-ray observations [68], it has been shown that the pulsars with reasonable parameters can explain the positron fraction as well as the electron plus positron flux data [69]. Therefore in this work we first fit both data set with the background plus pulsar-like models, and then add the DM contributions from IHDM to calculate their likelihoods [70]. The framework for doing such calculation in this astrophysical setting can be found in [71]. Basically, a Markov Chain Monte Carlo (MCMC) based global fitting tool was used to determine the model parameters. The observational data used in the fit include the AMS-02 positron fraction [37], PAMELA electron spectrum [66], and the total e + e − spectra of Fermi-LAT [40] and HESS [64]. Note that for the background electron spectrum we employ a three-piece broken power-law function in order to fit simultaneously the above data [71].
The solar modulation affects the fluxes of the particles at low energy. In this work we simply adopt the force-field approximation to account for the solar modulation effect [72]. It was found that the modulation potential Φ ≈ 970 MV can fit both the positron fraction and electron spectra. However, for the cosmic ray protons, a smaller modulation potential Φ ≈ 500 MV is favoured by the PAMELA data [71,73]. We leave this as an open question because the solar modulation may indeed depend on Also shown are the positron fraction data from AMS-02 [37], PAMELA [38] and Fermi-LAT [39], and electron flux data from Fermi-LAT [40], HESS [64] and PAMELA [66].
the mass-to-charge ratio of particles. The best-fitting positron fraction and electron spectra compared with the observational data are shown in Fig. 1. The model fits the data well and the reduced χ 2 is about 0.92.
When calculating the likelihood after adding the DM contributions in IHDM, we further multiply a factor of α i E β i to the fluxes of the background components (i = 1, 2, 3 for the e − background, e + background and pulsar e ± respectively), in order to take the uncertainties of the modelling into account [74]. The parameters α i and β i are left free and treated as nuisance parameters in our analysis. They are allowed to vary in the range of 0.1 < α i < 10 and −0.5 < β i < 0.5 to calculate the maximum likelihood of a specific DM model point.
• Cosmic ray antiprotons: The precise measurement of the antiproton-to-proton ratio and antiproton flux by PAMELA show relatively good agreement with the cosmic ray background model expectation [41,75], which leaves limited space for the DM models [76]. We calculate the expected antiproton flux in the same propagation model used to explain the e + e − data, as shown in Fig. 2. The solar modulation potential is adopted to be 500 MV as suggested by PAMELA [71,73]. Same as the α i and β i in e + e − case, an adjustment factor αpE βp with nuisance parameters αp and βp varied in the same respective range is employed to account for the uncertainties of the background estimation.  [77], BESS00 [78], BESS02 [79] and PAMELA [41].
In Table I, we summarize all the experimental constraints mentioned in this and previous section. To avoid words cluttering in later presentation, we denote the first block of relic density and collider constraints together with the theoretical constraints as RC (Relic density and Collider), the second block of LUX constraint as DD (Direct Detection) and the third block of constraints as ID (Indirect Detection). Additionally, we reject those points during our parameter scans which violate any one of the theoretical constraints on IHDM mentioned in section II B. We note that the data in the RC block does not involve large theoretical uncertainties compared with the other two blocks, so we will take special care of this block by including it only at the scan level.

V. METHODOLOGY
In this section, we will describe the statistical treatment of all the experimental constraints discussed in previous two sections and the numerical method used in our analysis. At the fitting level, we use the following different likelihood distributions: Gaussian, Poisson, and error function, depending on which experiments as shown in the fourth column in Table I  LUX and invisible Higgs decay width where only upper limits are provided, it is difficult to implement Poisson likelihood in the analysis. Under these circumstances, we will follow the procedure described in [80,81], where the error function was used to smear the experimental bounds.
• Gaussian likelihood distribution: The Gaussian likelihood distribution is related to the χ 2 as with the χ 2 defined as usual where σ is an experimental error and τ is a theoretical uncertainty. We assume that the theoretical uncertainty τ owes to either the discrepancy between computations using different methods or unknown high order corrections or non-perturbative uncertainties.
See Table I for the list of experiments that we use the Gaussian likelihood distribution.
• Poisson likelihood distribution: Regarding the LHC monojet, we use a Poisson likelihood distribution augmented with an extra Gaussian distribution to account for the background uncertainties. The probability distribution for each p miss T threshold is then written as where i refers different missing transverse energy E T cuts described in [54]. We also use the values of background events b with error δb and observed events o from Ref. [54].
To simulate signal events s, we use MadGraph 5 [82] to compute the cross section at the parton level and apply the appropriate cuts. Following the CMS study [54], we will use the following basic selection requirements for the transverse momentum (p j T ) and pseudo-rapidity (η j ) of the monojet:  While we also use the normal Poisson distribution to be the likelihood function for the γ-ray from dSphs, a half Poisson distribution is used for the γ-ray from GC. In other words, if the signal events are less than the number of events required for the maximum likelihood, we set its likelihood to be the maximum likelihood. This is because a normal Poisson likelihood of γ-ray from GC would give a very significant signal at m χ ∼ a few GeV [83]. Since the GC is a very complicated astrophysical environment, it is not clear whether such an excess is due to some kinds of astrophysical background or genuine DM signals. In order to be less biased, we therefore adopt a half Poisson distribution for our GC γ-ray likelihood. Moreover, the halo profiles in GC can also lead to big uncertainties. In this study, we use the isothermal halo profile in order to achieve a more conservative limit.
• Error function: Instead of using a step function, we employ an error function (erfc) likelihood with a theoretical error τ = 10% to smear the upper bound on the branching ratio of the invisible Higgs decay width BR(h → invisible), For the upper limit of LUX for the χ-nucleon cross section σ SI p versus the DM mass, we set τ = 150% for the hadronic uncertainties to account for the difference between the default value used in MicrOMEGAs and 1σ lower limit of the pion-nucleon sigma term σ πN obtained from lattice calculation [84].
With the above set up of the likelihood distributions for each experiment, we are able to guide our random scan of the parameter space to explore regions with high likelihood probability. The total likelihood is the product of all the individual likelihood from each experiment. As noted earlier, since DD and ID experimental constraints could suffer from large theoretical uncertainties (e.g. in the hadronic matrix elements in DD and DM halo profiles in ID), we rather play safe and conservative by including only the first RC block in Table I in the likelihood at the scan level.
Engaging with MultiNest v2.18 [85] of 20000 living points, a stop tolerance factor of 10 −4 , and an enlargement factor reduction parameter of 0.8, we perform 6 random scans in the six dimensional parameter space which will be restricted in the following ranges for the masses 122.0 ≤ m h / GeV ≤ 129.0 , and the following ranges for the couplings Of the total 6 random scans, 3 of them we use flat priors for all the above six parameters, while for the rest of the scans, we use flat priors for m h and λ L and log priors for the other four parameters. We note that coverage of the parameter space is the most important aspect for profile likelihood method. We combine these 6 different scans to perform our analysis in order to achieve better coverage of the parameter space and obtain accurate best-fit points.
In order to scan the parameter space more efficiently, we set the range of λ 2 up to 4.2 allowed by the unitarity constraint of Eq. (20). We finally collect ∼ 1.2 × 10 6 points in these scans.
In the next two sections, we will present our results mainly based on "Profile Likelihood" method [86]. Under the assumption that all uncertainties follow the approximate Gaussian distributions, confidence intervals are calculated from the tabulated values of δχ 2 ≡ −2 ln(L/L max ). Thus, for a two dimension plot, the 95% confidence (2σ) region is defined by δχ 2 ≤ 5.99.
We note that the best-fit points in either log or flat prior scan can have almost the same L max of individual scan but the locations of m S and m A are quite different from these 6 scans. This is due to the fact that we allow the LOP m χ to be either m S or m A . Same value of m χ corresponds to two positions in m S for LOP is S or not. Similar situation is found for m χ = m A depending on whether LOP is A or not. However, for the projection to m χ , the best-fits locate at the same region.

A. Low dark matter mass scenario
In this subsection, we will discuss the low DM mass scenario where the invisible Higgs boson decay is open either by h → SS or h → AA and study the implication from the LHC constraint on such invisible Higgs boson decay as well as LUX and relic density constraints on the hχχ coupling.
Let us first give the analytical expression of the invisible Higgs boson decay branching where Γ SM (h) is the total width of the SM Higgs boson taken as Γ SM (h) = 4.02 MeV in what follows, and with g hχχ given by Eq. (13).
In order to understand the correlation between the coupling g hχχ ∝ λ L,A and the invisible Higgs boson decay branching ratio, we illustrate in Fig. 3  In fact, it is plausible to relate BR(h → invisible) to the spin-independent cross section σ SI p for direct detection. In the IHDM, the diagram contributed to σ SI p is given by the tchannel Higgs boson exchange and so it is proportional to g 2 hχχ [87]. From the expression of BR(h → invisible) one can then eliminate the g 2 hχχ coupling in favour of σ SI p and other where For a given f (m N , m χ , m h , f N ) and BR(h → invisible), one can then calculate σ SI p (see [88] for a similar discussion in the framework of portal models).
We illustrate in Fig. 3 (right) a contour plot for BR(h → invisible) in the plane (m χ , σ SI p ) where we have used f N = 260 MeV which is roughly the default value used in MicrOMEGAs.
We show contour lines for BR(h → invisible) = 30%, 20%, 10% and 5%. Also shown is the actual limit from XENON100 and LUX as well as the projections from XENON1T experiments. It is remarkable from this plot that BR(h → invisible) > 30% is excluded by XENON100 if m χ is in the range of 20-60 GeV, while m χ in the range of 12-32 GeV with BR(h → invisible) > 10% is now excluded by LUX. Combining these two plots of Fig. 3, we can conclude that |λ L,A | should be less than about 2 × 10 −2 for the three experimental constraints of Higgs invisible width from LHC, LUX limit on σ SI p and relic density from PLANCK to be consistent with each other. Future sensitivity of the XENON1T experiment would be able to exclude invisible Higgs decay branching ratio as low as 1% or less, which can further constrain the couplings λ L,A that control the communication between the inert and visible sectors.

RC
We will use the next three figures to discuss the two dimension profile likelihoods from the RC block.
A: Fig. 4 First, in Fig. 4, we present the two dimension profile likelihood on the (m S , m A ) plane (left) and (m LOP , m H ± ) plane (right). The contours correspond to the 95% C.L. of RC constraints. For the area above the red-dashed line, S is the LOP; while below the red-dashed line, A is the LOP. Generally speaking, the relic density is a strong constraint, since we treat it as a positive measurement with a very small experimental uncertainty rather than an upper limit. For all the parameter space, we found that the DM relic abundance Ω χ h 2 is mostly too large, namely, its annihilation in the early Universe is too inefficient. Certain mechanisms, whether they are natural or not, have to play some peculiar roles to enhance the annihilation cross sections so as to reduce the relic abundance. These mechanisms can be clearly identified by the several different branches in the left panel of Fig. 4:  However, inefficient annihilation is not the case at 100 GeV < m χ < 500 GeV which has actually too little relic density (see also Fig. 6 of [24]). In fact, this is because the plane. We found that in this nearly box-shaped region, the EWPT T constraint will require the mass splitting m H ± − m A ≤ 250 GeV in the 3σ region. However, there is another limit m A − m H ± ≤ 400 GeV resulting from λ A < 4 (see later for further discussion of the λ A limit shown in the upper right panel of Fig. 5). In addition, we impose the condition m A + m S > m Z in order to escape the precise measurement of the Z 0 decay width from LEP as well as the search for neutralinos at LEP adapted here to the IHDM process e + e − → SA as was done in [31]. B: Fig. 5 Next, we discuss the limits on the two couplings λ L and λ A which play the role connecting the inert sector with the visible SM sector. In the upper left and upper right panels of Fig. 5, we show the 95% confidence level region (cyan dots) with the RC constraints projected on the (m χ , λ L ) and (m χ , λ A ) planes respectively. In our analysis, we do not specify S or A must be a LOP before the scan. We tolerate either to the fact that we take λ L as input parameter while λ A as output parameter, given by a combination of λ L , m S and m A via Eq. (11). From Eq. (11), we can see that when S is the LOP, λ 5 is negative so that λ A is greater than λ L . On the other hand, A is the LOP. Therefore, λ A will always have a wider range than λ L . From the two plots in the upper panel of Fig. 5, one can see that for RC constraints the allowed parameter space of λ L is also highly restricted compared to that of λ A . The additional parameter space for λ A at Higgs resonance appears only if A is the NLOP.
Because of m A − m S > 10 GeV, the λ A coupling being an output parameter according to Eq. (11) implies a very low abundance of A and therefore is not very sensitive to the relic density likelihood function.
Generally speaking, the allowed ranges of λ L and λ A for a given mass range of m χ can be similar (but not identical) if one allows either S or A to be the LOP. We illustrate this further using the two plots in the lower panel of Fig. 5 where the profile likelihood on the (m χ , λ χχ ) is shown, with left and right panels for m χ ≤ 100 GeV and m χ ≥ 500 GeV respectively. In these two plots, we can see that the 95% confidence level regions for the RC constraints applied in the (m χ , λ χχ ) plane are mostly symmetric but with some small asymmetries, especially in the small mass region of m χ ≤ 100 GeV. In the lower left plot of Fig. 5 where 65 < m χ < 100 GeV, a negative λ χχ is required to guarantee the cancellation between the contributions from different diagrams in the W + W − (or ZZ) channel such that a correct relic abundance can be achieved [25].
From these two profile likelihood plots on the (m χ ,λ χχ ) plane, three different limits on λ χχ can be summarized as follows: m χ ≤ 63 GeV: The upper limit of λ χχ in this region is due to the invisible Higgs boson decay width being too large. This limit is roughly |λ χχ | ≤ 0.026. The impact from the current monojet data is not strong. We have checked that it can constrain |λ χχ | from 0.03 -0.026.
m χ ≥ 500 GeV: As seen in Fig. 4, the relic density reduction at m χ > 500 GeV region is mainly resulting from the S − A, S − H ± and A − H ± coannihilation. In addition, the W + W − final state is being suppressed by increasing m χ . Therefore, we can see λ χχ is increasing with respect to m χ in order to maintain correct relic density. The limit depends on m χ and is in the range of |λ χχ | ≤ 1.1. The upper limit increases for higher m χ . One can work out these lower limits from the theoretical constraints, Eqs. (14) and (20). C: Fig. 6 Third and last for this subsection of RC, we discuss the diphoton signal strength constraint from the LHC. As reported by many studies, most of the ATLAS and CMS data are consistent with SM predictions. However, there are some small discrepancies between ATLAS and CMS results as far as the diphoton channel is concerned. While the ATLAS result shows some small excesses with respect to SM value, the CMS result which is based on multivariate analysis is nevertheless consistent with SM. Here, we do not tempt to explain the ATLAS excess by the additional charged Higgs boson loops in IHDM but instead we would like to show the points that satisfy δχ 2 < 5.99.
It is well known that in the SM, h → γγ is dominated by W ± loops which interfere destructively with the subdominant top quark loop. In IHDM, the charged Higgs boson loops can be constructive or destructive with the W ± contributions depending on whether λ 3 < 0 or λ 3 > 0 respectively [27,28]. As we showed before R γγ in the present case can be reduced to the ratio of the IHDM and SM branching ratios (see Eq. (23)). Thus once the invisible decay h → χχ is open, as long as the partial width of h → γγ has a comparable size with the SM one, the ratio R γγ will always be suppressed, i.e. R γγ ≈ Γ SM (h)/(Γ SM (h) + Γ(h → χχ)) < 1.
In the left and right panels of Fig. 6 we present the signal strength R γγ as a function of the coupling between the SM Higgs boson and a pair of charged Higgs bosons g hH ± H ∓ = −vλ 3 and of the charged Higgs boson mass respectively. The green band indicates the CMS result with 1σ uncertainty. In both panels of Fig. 6, we have the blue and red dots for the branching ratio of the invisible Higgs boson decay being larger and smaller than 20% respectively. On the other hand, if the invisible decay is close, one can see some small enhancements of R γγ > 1 for negative λ 3 (left panel).
Taking the relic density within 2σ range from Eq. (24) as well as the invisible decay branching ratio to be less than 65% (with 11.18% uncertainty obtained by adding in quadrature the experimental and theoretical errors given in Table I), we find that R γγ falls in the range 0.3 to 1.04. This upper limit of 1.04 for R γγ from the relic density constraint was already reported in [27,28]. Most of the points are within CMS 1σ band except for a few points with branching ratio of the Higgs invisible decay larger than 20% which are already excluded. Overall, our results agree with Ref. [24]. allowed region by RC constraints and the red dots are 2σ allowed region by RC+ID constraints.

RC+ID
We now move on to study the impact of DM indirect detection on the parameters m χ and velocity averaged annihilation cross section σv , where v is the relative velocity of the annihilating DM. Nowadays, the DM relative velocity is non-relativistic, one can simply use the approximation σv = σv| v→0 . In Fig. 7, we show the two dimensional profile likelihood on the (m χ , σv ) plane. The blue squares are 2σ allowed region by RC constraints and the red dots are 2σ allowed region by RC+ID constraints.
First, we can see three main branches, two vertical branches at 2m χ ∼ m h region and one horizontal at m χ 500 GeV region. They are corresponding to two different mechanisms to produce the correct relic density as discussed before. Comparing with Fig. 4, the first vertical branch at m χ < 60 GeV is S − A coannihilation but the second vertical branch at 60 GeV < m χ < 100 GeV is Higgs resonance region plus the openings of the W + W − and ZZ channels. The horizontal branch is again the coannihilation region. The thermal averaged σv T of the vertical branches are more p-wave (velocity dependent) so that most of the points can have wider spread values of σv . On the other hand, the horizontal branch is more s-wave (velocity independent) so that σv ∼ a few × 10 −26 cm 3 · s −1 .
Clearly, we can see that at the low m χ region (the two vertical branches) where the IHDM DM has larger σv the constraints from ID can further reduce the parameter space from the RC block only. In the first branch, ID constraints can even make σv having a value as low as 10 −27 cm 3 · s −1 .

RC+DD+ID
On top of the RC+ID constraints, we can further include the DD constraint from LUX.
In the left panel of Fig. 8, the 2σ allowed region on the (m χ , σ SI p ) plane by RC+DD+ID constraints is shown in red circles. The region of gray crosses was excluded by the LUX result with the hadronic uncertainties included. In IHDM, only t-channel with the h exchange can contribute to DM-quark elastic scattering. Therefore, one can expect the gray crosses region is due to the coupling λ L,A being too large. Interestingly, in the right panel where we map to the (m χ , σv ) plane, we can see that the LUX limit can only remove some regions (gray crosses) with low m χ which have large σ SI p (left panel) but the region (red dots) with σv as high as 8 × 10 −26 cm 3 · s −1 is still allowed! In addition, in the left pane we also plot the projected sensitivity of XENON1T which has the potential to probe the higher mass coannihilation region. We will discuss this impact further in section VII.
In Fig. 9, we show the 1D relative likelihood distributions for m S (upper left), m χ (upper right), m H ± (lower left) and λ χχ (lower right) in the three blocks of RC, RC+ID, and RC+ID+DD, marked by black dash-dot, blue dash, and red solid lines, respectively. The relative likelihood in each case is defined as L/L max where L max is the likelihood at the best-fits. We do not show the distribution of m A since it is almost identical to m S . As aforementioned that m χ can be either m S or m A , the peaks at m χ < 100 GeV in the upper right panel correspond actually to two separated peaks with almost the same height at m S < 300 GeV in the upper left panel. The first peak owes to m χ = m S and the second m χ = m A . We can see clearly that there is no preference of m χ = m A or m χ = m S .
Since the γ/e + /p fluxes are inversely proportional to m 2 χ , the impact of ID constraint is mainly on the lower m χ region. On the other hand, if m χ turns out to be too large suppressing the DM signal, the total ID χ 2 will be the same as consideration of background only. From Fig. 9, we found that with the additional DM signal, the χ 2 can be improved to at most 1σ significance. For example, in the upper right plot, we can see that at the m χ > 500 GeV region there is a flat RC likelihood distribution while the RC+ID one is decreasing. Because of χ − H ± coannihilation, we can see similar decrease of the RC+ID likelihood distribution for the m H ± > 500 GeV region in the lower left plot. Note that this large m χ region can not be constrained by the current LUX data. There is a third peak at m χ ∼ 500 GeV because the m χ < 100 GeV region is less favored by LUX. Even though the best-fit point still locates at this lower mass region, the minimum χ 2 is roughly increased by one unit. As a result of increasing the minimum χ 2 , the relative likelihood of the m χ > 500 GeV region becomes statistically more significant.
In Table II     of S − H ± coannihilation case, the distribution of different channels contributed to the relic density is quite spread out in this case. Thus, beside the Higgs resonance point, the other coannihilation channels can lead to effective relic density reduction as well. Finally, we also show in Table II the ID δχ 2 for these four benchmark points. We note that poorer values of δχ 2 p are obtained at the first two benchmark points (S − A coannihilation and Higgs resonance) where the bb final state dominates in the antiproton flux. While the bb mode can be significant for the antiproton flux from the fragmentation of b andb into antiproton, the smallness of the b-quark parton distribution inside the nucleon makes the b-quark has very small impact on the σ SI p . On the other hand, values of σ SI p at these two benchmark points are quite acceptable.
In Table III, we summarize the best-fit points for the three different blocks from our scan.
The second column is only with RC constraints in the likelihood while the third and fourth   Note that the invisible Higgs decay is closed at these three best-fit points.
columns are with RC+ID and RC+DD+ID in the likelihood, respectively. We would like to stress that there is no preference of χ = S or χ = A due to the symmetry between S and A in the model. We find that the maximum likelihood of L(χ = S) and L(χ = A) are roughly the same. Therefore, the fact that the best-fit points are located at χ = S or χ = A region is just due to the fact that we collected the maximum likelihood before hitting the sampling stop criteria. In other words, we cannot tell the dark matter in IHDM must be a scalar or pseudoscalar from this analysis. However, we can see that the best-fit points  data. The orange square will still be allowed by 100 fb −1 data but disfavoured by 300 fb −1 data.
The red dots will be allowed by 300 fb −1 data. They are all in 2σ significance. than the astrophysical background. As seen from Figs. 1 and 2, there are still some rooms for DM in indirect detection experiments. Perhaps not a discovery with large statistical significance, but a weak signal usually fits the likelihood better than using the background only hypothesis. Certainly, our understandings of the astrophysical backgrounds could be too naive. In Fig. 10, we present the potential power of LHC monojet search with 100 fb −1 and 300 fb −1 on the (m χ ,λ χχ ) plane. In linear scale, we zoom into the region m χ < 63 GeV where the invisible Higgs decay is open. All the points shown satisfy the RC+DD+ID constraints in 2σ. With 100 fb −1 of data, only the orange boxes will be allowed while the few black crosses located near the boundary where |λ χχ | ∼ 10 −2 will be disfavoured in the 2σ subset.
However, with 300 fb −1 of data, the range of λ χχ will be extended to the region of red dots in Fig. 10 where |λ χχ | 6 × 10 −3 .

B. XENON1T
In Fig. 11, we show the disfavoured region by future XENON1T sensitivities subjected to the RC+ID+DD constraints in 2σ significance. The left panel is for (m χ , λ χχ ) and the right panel is for (m χ , σv ). The red dots are favoured but gray dots/crosses are disfavoured by XENON1T limit. Although the region of m χ > 500 GeV can not be entirely ruled out by XENON1T from our global analysis based on tree level calculation, a recent paper [89] pointed out that electroweak corrections can significantly alter the theoretical prediction of σ SI p , especially for large m χ region. As shown in their computation, σ SI p is not expected to be lower than 10 −11 pb even when one loop corrections are included [89]. We thus expect next generation of ton-sized detectors for DM direct detection can probe most of the parameter space of IHDM.  σv ) planes respectively subjected to the RC+ID+DD constraints in 2σ significance. The red (gray) area will be allowed (excluded) by XENON1T sensitivity.

C. AMS-02 antiproton
We generate the simulated one year AMS-02 data of the antiprotons following Ref. [90].
The expected antiproton flux φ is adopted to be the one described in section II (see Fig. 2).
The number of antiproton events in a given energy bin is approximately where A(E k ) is the simulated geometry factor given in [91], ∆E is the width of the energy bin and ∆t is the exposure time. We generate the data from 1 to 300 GeV, with 50 bins logarithmically evenly distributed according to the binning of the positron fraction measurement by AMS-02 [37]. For the "observed" number of events we apply a Poisson fluctuation on Np, with statistical error ≈ 1/ Np. The systematic error is simply adopted to be ∼ 5% [90], which is added quadratically to the statistical error. The simulated antiproton flux for one year observation of AMS-02 is shown in the left panel of Fig. 12. Using the simulated antiproton data, we calculate the χ 2 of each DM model point with the same method described in sections IV and V. In the right panel of Fig. 12, the exclusion power of the AMS-02 one year antiproton data is shown. The red dots are allowed but gray crosses are disfavoured by future sensitivity. Comparing with the exclusion power of XENON1T sensitivity (right panel of Fig. 11), we can see most of parameter space excluded by AMS-02 antiproton data are also excluded by XENON1T. However, for the σv ∼ 2 × 10 −26 cm 3 · s −1 at the Higgs resonance region (near the top of the second vertical branch from the left), one can find some small fractions of red dots that can be excluded by AMS-02 antiproton data but not yet ruled out by XENON1T. This is because the DM annihilation channels are dominant by τ + τ − or bb final state at these points. However the hτ + τ − coupling is irrelevant to direct detection and the hbb coupling can contribute to direct detection only by integrating this heavy b quark to obtain the hgg coupling. Hence its contributions to σ SI p is also small as compared with light quarks. We finally show in Fig. 13 the total impact from the combined sensitivities from the above three future experiments on the (m χ ,λ χχ ) plane. For the LHC-14 monojet, we will assume 300 fb −1 of data in making these two plots. Left and right panels correspond to m χ less than 100 GeV and greater than 500 GeV respectively. With all three future experiments sensitivities, from the left panel of a zoomed-in view of low m χ region, we see that the lower limit of m χ is lifted slightly from 52 GeV to 55 GeV. In this low mass region where the invisible decay h → χχ is open, while we do not found any upper limit on m χ , λ χχ is found to lie between −5 × 10 −3 and 3 × 10 −3 . On the other hand, if the invisible mode is closed, the upper and lower limit of λ χχ is varied with respect to m χ (right panel). Comparing with current experimental data, these three future experiments sensitivities are robust but neither the lower m χ region nor the larger m χ region can be entirely ruled out.

VIII. CONCLUSIONS
Despite IHDM was proposed more than three decades ago, it is still one of the most simplest models and yet viable for scalar dark matter. We have performed a global fit analysis on this model. This analysis has been performed in light of the recent ATLAS and CMS discovery of a 125-126 GeV Higgs-like particle, taking into account the recent relic density measurement by PLANCK, DM direct detection from LUX and indirect detection from PAMELA, Fermi-LAT and AMS-02.
We have shown that the constraint from DM direct detection search, such as the latest LUX upper limit of year 2013, provides a robust constraint on the parameter space. In particular, if the invisible decay of the SM Higgs boson is open, the upper limit of the Higgs invisible width from LHC together with the LUX constraint could put some interesting limits on the SM Higgs boson couplings to the DM in IHDM. Indeed, an invisible decay of the SM Higgs boson with a branching ratio larger than 30% and a scalar dark matter mass within the range of 20-60 GeV are excluded by current data.
We emphasize that there is no preference of χ = S or A in our study. However, we found that m χ 100 GeV region is slightly favoured by EWPT and ID constraints than m χ 500 GeV region. In addition, in the 95% C.L. of RC+DD+ID constraints, m χ has the lower limit around 52 GeV. We also note that the likelihoods obtained in this work were obtained using the tree level relation for λ L and λ A (Eq. (11)) and the tree level formula for the coupling g hχχ (Eq. (13)).
Higher order corrections will necessarily modify these relations and hence the relic density prediction will be affected. The profile likelihoods for the IHDM will be modified as well.
Although loop corrections have been shown to affect significantly the DM scattering crosssection on nucleons in the IHDM [89] and thus modify the impact of direct detection searches on the viable parameter space of the model, it is beyond the scope of the present analysis to take them into account. One should bear in mind that such corrections will also probably affect the positions of the best-fit points.
In summary, we note that the overall shapes of the 95% C.L. contours presented in this work are mainly determined by the PLANCK relic density measurement. LHC monojet is only relevant when the invisible decay of the Higgs is open, in which case we obtain the limit for the coupling λ L,A ≈ 10 −1 which is not very stringent. On the other hand, our best-fit points are located at m χ ≈ 70 GeV and so do not allow the opening for invisible decay of the SM Higgs into DM. The current ID and DD data are only sensitive to Higgs resonance region. Except for relic density constraint, currently no other experimental data sets are sensitive to the IHDM parameter space at m χ 500 GeV. However, one expects future XENON1T can probe this region. Moreover, future instruments such as DAMPE, GAMMA-400 and CTA will test this higher m χ region as well [92].
As mentioned previously, experimental search for the inert Higgs (neutral and charged) behaves like SUSY search for charginos and neutralinos. Therefore, one of the most popular signatures for inert Higgs searches would be also trilepton and/or dilepton plus missing E T [30,93]. A dedicated analysis for the IHDM has been performed in [30] where it has been demonstrated that the experimental reach for the inert Higgses is only about 300 GeV which is somewhat smaller than the LHC reach for the charginos and neutralinos. The main reason is that the cross section for the scalar pair production pp → H ± A 0 is smaller than the gaugino pair production pp → χ ± 1 χ 0 2 . As we have seen in our analysis, inert Higgses with masses ≥ 0.5 − 4 TeV are consistent with all experimental and theoretical constraints. One concludes that the IHDM is here to stay for another decade.
The IHDM can be further extended by including inert right-handed neutrinos with Majorana masses [16]. Masses for the SM light neutrinos can be generated through radiative processes with only inert particles running inside the loop. This extension of IHDM would exhibit intricate interplay between dark matter and neutrino physics. Detailed global analysis of this extended model is also quite interesting and will be presented in a future publication.