Excluding the Light Dark Matter Window of a 331 Model Using LHC and Direct Dark Matter Detection Data

We sift the impact of the recent Higgs precise measurements, and recent dark matter direct detection results, on the dark sector of an electroweak extension of the Standard Model that has a complex scalar as dark matter. We find that in this model the Higgs decays with a large branching ratio into dark matter particles, and charged scalars when these are kinematically available, for any coupling strength differently from the so called Higgs portal. Moreover, we compute the abundance and spin-independent WIMP-nucleon scattering cross section, which are driven by the Higgs and $Z^{\prime}$ boson processes. We decisively exclude the $1-500$~GeV dark matter window and find the most stringent lower bound in the literature on the scale of symmetry breaking of the model namely $10$~TeV, after applying the LUX-2013 limit. Interestingly, the projected XENON1T constraint will be able to rule out the entire $1$~GeV-$1000$~GeV dark matter mass range. Lastly, for completeness, we compute the charged scalar production cross section at the LHC and comment on the possibility of detection at current and future LHC runnings.


I. INTRODUCTION
The nature of the dark matter (DM) is one of the greatest puzzles in current science, once the DM constitutes approximately 23% of the Universe budget. There are promising ongoing searches with the aim of detecting and finding the nature of the DM that permeates the Universe. There are many dark matter candidates in the literature, but the most seemingly promising ones are the so called WIMPs (Weakly Interacting Massive Particles) for having a thermal cross section at the electroweak scale, naturally addressing the structure formation process, and being predicted in many interesting particle physics models.
There are four different methods to infer the presence or detect theses WIMPs known as indirect detection, direct detection, colliders and cosmological effects. Indirect detection searches have found some excess events in the gamma-ray emission [1] and in the cosmic ray emission [2] which might be explained by annihilation of WIMPs in our galaxy [3]. Likewise, some direct detection experiments such CoGeNT [4], DAMA [5], CRESST [6] and most recently CDMSII-Si [7] have observed some excess events consistent with WIMP scatterings [8]. Due to some possible leakage of background events into the signal region at low energies and the nonobservation of such events in the XENON [9] and LUX [10] experiments, those events do not constitute an irrefutable DM signal [11]. Furthermore, there are cosmological measurements of the Cosmic Microwave Background that revealed some degree of dark radiation observed in the Planck data [12] among other satellites [13] that may constitute an evidence for a sub-dominant non-thermal production of DM [14]. Lastly, collider data, which provide an important and complementary method to infer the nature of the dark matter have not observed any positive signal for a stable particle and just bound on the mass and coupling strengths were derived [15]. * diegocogollo@df.ufcg.edu.br † agonzalez@ucsc.edu ‡ fdasilva@ucsc.edu § patricia.rebello.teles@cern.ch Here we will focus on a particular extension of the SM namely, 331LHN that might address these evidences. 331LHN stands for a electroweak extension of the SM where doublets are replaced by triplets in the scalar as well as in the fermion sector. This proposal has been able to endure all electroweak precise measurements and reproduce the SM results concerning the Higgs signal strength [16] as oppose to other 331 model extensions which predicted a H → γγ enhancement [17]. It has a rich particle spectrum comprised of charged scalars and gauge bosons, sterile neutrinos and exotic quarks with interesting phenomenological aspects, which had been investigated elsewhere [19]. Furthermore, this model as oppose to previous versions [20][21][22][23][24][25] does have a plausible DM candidate able to explain the gamma-ray excess observed in the Fermi-LAT data at the Galactic Center [1] and offers a plausible mechanism to account for the dark radiation observed by the Planck Collaboration through a sub-dominant non-thermal production of WIMPs [26] while evading structure formation, Big Bang Nucleosynthesis and CMB bounds among others. An extensive analysis concerning the heavy fermions present in the model has been done and stringent bounds on the mass of the lightest Sterile neutrino have been found as a function of the Z mass in Ref. [27] and in a model independent fashion in Ref. [28]. It is important to stress that these constraints on the Z mass do apply at some level to all 331 models that have fermions as DM candidates, as discussed in Fig.7 of Ref. [27] and are complementary to others coming from colliders [29] mostly focused on the Z boson, FCNC [30], muon decay [31] and Top decay [32] analyses.
That being said, here we will discuss the 331LHN model which is a viable alternative to the SM because besides being able to reproduce the well tested SM results and has a DM candidate, differently from other 331 proposals in the literature. It has already been shown in Ref. [16,33] that his model may have two DM candidates, but they do not co-exist. Our purpose is to derive constraints on the dark sector of this model by investigating the role of the dark sector in the Higgs signal strength now the Higgs discovery has anchored. In particular, we will find important limits on the mass of the WIMP and charged scalars, and further compute their production cross section and comment on their potential discovery at the LHC.
The paper is organized as follows: in section II we will briefly introduces the 331LHN model. In sections III we will derive bounds on the dark sector of the model. In section IV we comment the possibility of detection at current and future LHC runnings, going to the conclusions afterwards.

II. THE 3-3-1LHN MODEL
3-3-1 stands for an extension of the electroweak sector of the Standard Model where the electroweak sector SU (2) As a result the doublets in the electroweak sector of the SM will be replaced by triplets. This extension is motivated by important matters not addressed by the SM such as the number of generations, neutrinos masses and for not providing a plausible DM candidate. Moreover, it reproduces precisely the SM results including the Higgs properties as shown in Ref. [16]. Hence the 3-3-1LHN remains as a compelling extension of the SM. We will not dwell on unnecessary details, instead we will shortly review the key points of this model hereafter which will allow the reader follow our reasoning.

Leptonic Sector
The leptons are displayed in triplet and singlet representations as follows: where a = 1, 2, 3 runs over the three lepton families, and N a(L,R) are heavy fermions added to the SM particle spectrum. The shortened representation (1 , 3 , −1/3) simply refers to the quantum numbers of the symmetry group The SM mass spectrum will be reproduced. In particular, the charged leptons will have acquire mass terms through the first term of the Yukawa Lagrangian in Eq.(2), whereas the neutrinos through a dimension 5 effective operators according to Eq.(3).
where ρ, η and χ are the scalar triplets introduced in Eq. (11). We do not show explicitly the masses of the SM particles in this work and just present the mass of the heavy fermions (N a ) introduced by the 3-3-1 symmetry as follows, where g aa are the Yukawa couplings that appear in the last term of Eq. (2). We assume all Yukawa couplings to be diagonal with a normal hierarchy throughout this work. The hierarchy adopted does not lead to any impact on our conclusions though.

Hadronic Sector
As for the quarks in the theory, they are also arranged in triplets. In particular, the third generation lives in a triplet representation while the other two generations are in an antitriplet representation of SU (3) L , so that triangle anomalies are cancelled [20] as follows, where the index i = 1, 2 means the first two generations. The primed quarks (q ) are heavy quarks with the following electric charges, Q(q 1 ) = −1/3, Q(q 2 ) = −1/3, Q(q 3 ) = 2/3. These quarks do not couple with the SM gauge bosons but couple with the extra gauge bosons introduced by the 3-3-1 symmetry that we will discuss further 1 The masses of all quarks are derived from the Yukawa Lagrangian in Eq. (6), with i, j = 1, 2. and a = 1, 2, 3. Again, the SM quarks masses are equal to the usual ones, As for the three new quarks q a they have their masses given by the first two terms of Eq. (6) with, One can clearly see that the masses of the new quarks are proportional to the scale of symmetry breaking of the model which assumed to lie at the TeV scale. Anyway, the new quarks do not play any role in the current work and will be thus completely ignored henceforth.

Gauge Bosons
Due to the enlarged electroweak gauge group (SU (2) L → SU (3) L ) extra gauge bosons will arise in the 3-3-1LHN model called Z , W ± , and U 0 and U 0 † . These bosons have masses proportional to the scale of symmetry breaking of the model as, where we used the shortened notation sin θ W = s W and cos θ W = c W . Notice that their masses are also balanced by the scale of symmetry breaking of the model (v χ ).
It is important to mention that the Z does not couple to the SM fermions in the same way the Z boson does. In fact, the couplings of the Z with the SM quarks and charged leptons are dwindled in ∼ 50%, while with SM neutrinos are 80% suppressed in comparison with the Z-quarks/charged leptons and Z-neutrinos couplings respectively. In other words, the general neutral current, which can be written as, (9) have vector (g V ) and axial (g A ) couplings with quarks and leptons suppressed in comparison with Z couplings as aforementioned. This fact is important to emphasize because recent and stringent limits were derived on the mass of the Z boson for the 3-3-1 model with right handed neutrinos using CMS data [29], namely, M Z > 2.2 TeV. However, this constraint does not apply to our model because the Z here decays mostly into missing energy (heavy neutral fermions). For the regime where M Na < M Z /2, the Z decays at 100% into fermion pairs (N a N a ) as oppose to Ref. [29], which assumed that the Z decays primarily into quarks and charged leptons. Nevertheless, when N a N a channel is not kinematically accessible Z the results found in Ref. [29] do apply to our model. Either way, we will take this face value limit throughout this work. For more complete analyses concerning the phenomenology of this neutral boson we recommend Ref. [19].
As for the charged current it reads, Notice the presence of the new gauge bosons U 0 and W in Eq.(10). There is lack of collider bounds on the mass of this gauge boson U 0 . Nevertheless, their mass terms are the same according to Eq. (8), so that any constrain found on the mass of the W is applicable to U 0 as well. The W on the other hand has been vastly searched at the LHC [34,35]. From LEP-II implies M W > 105 GeV, because this charged boson could have been easily produced via drell Yan processes. From the ATLAS Collaboration we know that a W boson has been ruled out for M W < 2.55 TeV at 95% C.L, assuming SM coupling with fermions. Similarly to the Z case, this limit limit does not directly apply to our model for three reasons: (i) The boson W does not couple similarly to the SM W boson as can be seen in Eq. (10).
(ii) W decays predominantly into sterile neutrino plus electron (N e) pairs; (iii) In proton-proton collisions, the W production is different from the W one. There are additional processes in addition to Drell-Yan processes that contribute such as a t-channel process mediated by new quark q 1 , and three s-channel processes mediated by the Higgs, the scalar S 2 and the Z .
In summary one cannot straightforwardly apply the Z and W limits into this model. Anyhow, at which degree these bounds are applicable to the 331LHN is far beyond the scope of this paper. Here we aim to derive lower limits on the mass of the charged scalars of the models which we can surely be might lighter then the mass of this boson at the cost of some tuning in the couplings as we shall see in the next section.

Scalar Content
The symmetry breaking pattern SU (3) (11) which form the following scalar potential, with η and χ both transforming as (1 The scalar triplets above are invoked in order to generate masses for all fermions in the model after the spontaneous symmetry breaking mechanism represented by the non-zero vacuum expectation value of the scalars η 0 , ρ 0 and χ 0 as, There are additional neutral scalars in the spectrum, namely η 0 and χ 0 , which are enforced not to develop vevs in order to preserve the discrete symmetry given by, where d i and u 3 are new heavy quarks predicted in the model due to the enlarged gauge group. The remaining fields all transforming trivially under this symmetry. This parity symmetry can be understood as a R-parity symmetry quite similar to the one in the minimal supersymmetric standard model case, which we indicate with P = (−1) 3(B−L)+2s , where B is the baryon number, L is the lepton number and s is spin of the field. This discrete symmetry induce three distinct consequences. First, it stabilizes the lightest particle charged under this discrete symmetry. Second it simplifies the scalar mass spectrum of the model. Lastly but not least, it prohibits Yukawa mass terms that would mix the new quarks with the SM ones. The setback is that we rely on the assumption that the remaining neutral scalars η 0 and χ 0 do not develop a vev. This is a crucial assumption in what follows and an important discussion on this topic has been given in Refs. [27,36,37]. Moreover, a more elegant way to explain the WIMP stability would be gauging this discrete symmetry as discussed in Ref. [36]. Less appealing DM scenarios in 331 models have been studied elsewhere [39].
In the 3-3-1LHN model there are two possible DM candidates: a complex scalar φ (the mass eigenstate resulting from η 0 and χ 0 ) and a heavy fermion N i (the lightest of the new heavy neutrinos). We will restrain ourselves to the case where the scalar is our lightest particle protected by this R-parity and investigate the consequences of this choice in the dark sector of the model under the assumption that this scalar is a plausible DM candidate being able to reproduce the DM abundance as well as satisfy the direct detections bounds as had been shown in Refs. [16,27,33]. Anyhow, once the pattern of symmetry breaking has been established one can straightforwardly derive the mass eigenstates of the model. After spontaneous symmetry breaking the three CP-even neutral scalars mass eigenstates (H, S 1 , S 2 ) are found to be, where S 1 and S 2 are new CP-even scalars and have masses proportional to the scale of symmetry breaking of the model v χ , while H is identified with the SM Higgs boson. The vev v which appears in Eq. 15 must be equal to 246/ √ 2 GeV, in order to reproduce the right masses of the SM gauge bosons. We used in Eq.(15) λ 4 = λ 5 = 1/4 to just simplify the mass terms, but we emphasize that throughout this work we performed a numerical analysis without assuming any simplifying assumption regarding the couplings.
Besides the three CP-even scalars, a CP-odd scalar (P 1 ) shows up with the following mass: An additional complex neutral scalar also rises from the spectrum namely φ, with mass given by Lastly, because of the presence of charged scalar fields in the triplet of scalars in Eq. (11), two massive charged scalars h 1 and h 2 rise, with masses As one can see the scalar sector of the 331LHN model is rather rich. We have discussed and presented the mass spectrum of the model and identified the WIMP of the model so far. Further, we will derive bound on the dark sector of the model by using direct dark matter detection and LHC data.

III. BOUNDING THE DARK SECTOR
As we discussed in the previous section, the 3-3-1LHN model has a complex scalar (φ) as dark matter, i.e as our WIMP. The stability of our dark matter candidate is guaranteed by a R-parity symmetry described in Eq.14. In this work we are focused on the light mass window and in Fig.1 we exhibit all annihilation channels for a light WIMP. We have implemented the model in the Micromegas package [40], and computed the DM observables numerically. The abundance is determined by numerically solving the Boltzmann equation. Despite having many diagrams contributing to the abundance of our WIMP, we can clearly understand the role of the most relevant diagrams in Fig.1. As we know the abundance of our generic WIMP is inversely proportional to the annihilation cross section. Hence, the resonances in the annihilation cross section set the depths of the abundance. For instance, in Fig.2 we have shown the abundance of our WIMP as a function of its mass. The red (blue) curve induces a overbundant (underabundant) WIMP where overabundant (underabundant) means Ωh 2 > 0.12 (Ωh 2 < 0.11). The horizontal line is to draw the eye to the right abundance 0.11 ≤ Ωh 2 ≤ 0.12 according to Planck [12]. One can clearly see a resonance at M H /2. We have used a scale of symmetry breaking of v χ = 14 TeV in Fig.2. As we increase/ decrease the latter the curve barely changes. For this reason, shifting the scale of symmetry breaking will not change our results neither and most importantly the resonance at M H /2. Therefore, for a light WIMP the Higgs mass control the abundance. The remaining channels in Fig.1 are only relevant for heavier masses and for heavier WIMPs more diagrams now shown in Fig.1 become kinematically available.
As for the WIMP-nucleon scattering cross section, we find the result presented in Fig.3. The dashed curve is the LUX 2013 bound. It means that everything above the curve is excluded by the non-observation of dark matter scatterings by the LUX collaboration. It is obvious by Fig.3 that the Light WIMP scenario is way excluded by the current direct detection data, and for this reason our WIMP is not able to explain the few GeV gamma-ray Galactic Center excess observed in the Fermi-LAT data as claimed in Ref. [16]. Additionally, we will see further that the LHC data concerning the Higgs support our conclusion. After computing the DM observables we are going to discuss the impact of the Higgs precise measurements on this model. An interesting feature of this 331 model is that the Higgs couples to all scalars in the spectrum. Now that the Higgs discovery has been anchored and its properties well measured at 10% level we are able to constrain in a trivial way the mass of those new scalars by imposing the branching ratio of the Higgs into a pair of scalar not to exceed the current bounds. The masses of the scalars P 1 , S 1 , and S 2 discussed in the Section II are of the order of the symmetry breaking scale of the model, v χ . Since we are assuming v χ to be of few TeVs, the final states where one of these scalars are present will be kinematically forbidden. Therefore, the only scalars the Higgs might decay into are the charged scalar h ± 1 and the dark matter candidate φ.
Our goal in this work is to derive bounds on the mass of these scalars based on the current Higgs measurements and to explore the possibility of detecting them at LHC's current and future runnings. It has been previously shown that this scalar could be a potential explanation for the Galactic Center gamma-ray excess for the case that M W IM P 20 GeV [16]. Furthermore, we have noticed in Fig.3 that only a quite fine-tunned region of the parameter could allow such scenario since LUX bound literally slew the light WIMP scenario. Furthermore, as we shall see in FIG.4, this low mass regime is also entirely ruled out by current measurements concerning the invisible decay width of the Higgs. According to the most recent results from LHC, the branching ratios into invisible particles larger than 10% or so have been excluded [43], assuming that the Higgs production cross section equals its SM value. In this 331 model, the new quarks do not couple to the Higgs, therefore the production cross section is the same. In other words, from precise measurements of the Higgs signal strength at the LHC we know that there is no room for a large branching ratio into missing energy in our model. Nevertheless, in our model the Higgs is allowed to decay into a pair of WIMPs according to the decay rate where, In FIG.4 we exhibit the branching ratio of this channel as a function of the WIMP mass. One can realize from FIG.4 that the decay mode of Higgs into a WIMPs pair overwhelms all other channels yielding an unacceptable invisible branching ratio. Hence from the FIG.4 we conclude that the WIMP must be heavier than the M H /2, i.e 62.5 GeV, in order to have a branching ratio allowed by the current LHC bound.
Summing up • The Higgs production cross section is equal to the SM value, therefore we can straightforwardly constrain the branching ratio. • M W IM P > M H /2, in order to obey the LHC bound concerning the Higgs invisible width.
• LUX bounds slew the light dark matter window, supporting the aforementioned Higgs constraint.
In addition to the WIMP, the charged scalars h ± 1 are the remaining kinematically states that the Higgs can decay into. We aim to derive bounds on the mass of these scalars just by using the fact that the Higgs might decay into them with a large branching ratio. Afterwards we compute the production cross section of these scalars at several LHC energies and comment on the possibility of detecting them.
That being said, we firstly show the analytical expression for the decay rate H → h + 1 h − 1 , In FIG.5 we show the branching ratio of the Higgs into the pairs h + 1 h − 1 as a function of their masses. From the current Higgs data, there is no room for a Higgs decaying with a large branching ratio either into missing energy or into charged particles. Therefore we can impose an lower bound on the masses of these scalars just by looking at the Higgs branching ratio into these channels. Similarly to the dark matter case studied previously, from FIG.5 the lower bounds are M h ± 1 > 62.5 GeV. At this point it is important to note that, because the φ is enforced to be our DM candidate, the whole 331 mass spectrum is automatically heavier than our WIMP. Therefore this lower bound might turn out to be much stronger depending on the mass of the WIMP we are considering. Also, in order to have scalars with a mass around 60 GeV some tunning is required in the coupling λ 8 , according to Eq. (18). The level of finetunning is dictated and proportional to the scale of symmetry breaking of the 331 gauge symmetry. The total width of these charged scalars is exihibited in FIG.6. There we see that the charged scalars decaying with a branching ratio of 100% into the neutral heavy fermion (N) plus charged lepton pair (l). This feature is true as long as M h1 > M Na , where M Na are the masses of the heavy fermions which are assumed to be equal for simplicity. In  FIG.6 we have plotted the total width for M Na = 100 GeV (solid) and M Na = 300 GeV (dashed). Moreover, we have adopted v χ = 3 TeV. For such symmetry breaking scale, the remaining particles of the 331 model are heavier than h 1 . Therefore, the charged scalars decay with a branching ratio of 100% into the neutral heavy fermion (N) plus charged lepton pair (l). For the same reason, when M h1 < M Na the total decay width of the charged scalar is zero. The latter regime is problematic though, because long lived charged scalars would form the so called heavy Hidrogen that have strong abundance limits as discussed in Ref. [42]. The only kinematically suitable decay channel is h1 → laNa.

IV. SCALAR PRODUCTION AT THE LHC
The purpose of this section is to provide some results on the possible detection of the charged scalar at the LHC. The detection of our WIMP at the LHC is less likely due to the featureless signal, i.e, a large amount of missing energy. In FIG.7 we have computed the production cross section σ(pp → h + 1 h − 1 → lN a lN a ) at LO, using CalhHEP 3.4.3, with CTEQ6L as the default parton distribution function, for the LHC operating with center of mass energy of 7, 8 and 14 TeV assuming M Z = 1 T eV fixed. This production cross section is mostly driven by the Z mass. The relevance of this particle comes from its s-channel production.
From FIG.7 we recognize that the charged scalar production cross section falls steeply as its mass increases. Therefore its observation at the LHC seems attainable only for masses M h1 < ∼ 500 GeV. For the regime M h1 > M Ni , the branching ratio h 1 → l i N i is 100%. The coupling h + 1 l + N a is proportional to the masses of the heavy fermions and the charged leptons involved. Therefore, in the regime of degenerate heavy neutrinos masses, the τ N 3 channel overwhelms the other channels. Some deviations of the partonic level prediction are expected when detector effects and showering are included since, although the efficiency of the LHC detectors for events with hard electrons and muons, and large missing transverse energy can reach 96%-99%, the tau leptons are more difficult to detect, as there is a larger background from misidentified jets. Anyway, tau identification efficiency is larger than 65% for P τ T > 20 GeV. According Fig.7, the total cross section for the charged scalar pair production is around 0.25 pb at LHC8 with M h1 = 100 GeV and M Z1 = 1 TeV, while the LHC's current integrated luminosity is about 23.20 fb −1 , delivered till the end of 2012. Therefore, assuming the detector efficiency of the τleptons described above, we could expect around 3770 events in this LHC scenario.
Furthermore, as expected, this new particle is even more within the LHC14 setup, because the production cross section can reach the value of 0.7 pb for a M h1 = 200 GeV and M Z1 = 1050 GeV scheme, as we can infer from FIG.7, under the aforementioned assumptions. In fact, operating with its nominal integrated luminosity of L = 100 fb1 and assuming the same previous τ -lepton detection efficiency, we could expect around 45500 events for this channel.
It is important to point out that for sufficient heavy charged scalars the final states V + Z, V + Z , V + h, and U 0 W + , among others are kinematically possible. Nevertheless as we see in FIG.7, once we increase the mass of the charged scalars their production cross section becomes too suppressed, making their observation quite unlikely at the LHC.
In order to investigate the impact of increasing the Z mass we have plotted in FIG.8 the production cross section in the M Z × M h1 plane. As we expect the cross section decreases. From FIG.8 we observe keeping M h1 ∼ 200 GeV that the production cross section is 0.6 pb for M Z = 1.1 TeV, whereas for M Z = 3 TeV it goes down to 10 −2 pb.
In summary, the Higgs signal strength requires the mass of the WIMP, the CP-even scalar S 1 and the charged scalar (h 1 ) to be all heavier than ∼ 63 GeV. In addition, WIMP stability sets the mass of the latter scalars, demanding them to live at least say a couple of hundred GeV. At this mass scale the charged scalar seems to be within reach of the LHC at 8 and 14 TeV. Furthermore, if this plateau of null dark matter results remain and no compelling evidence for WIMPs pops up in the near future ruling out WIMP masses up to the TeV scale, the masses of neutral scalar S 1 and the charged scalar h 1 will have to compulsorily live at few TeV turning completely unlikely their observation at the LHC at 8 or 14 TeV under the assumption that φ is our DM candidate. For the regime M h 1 > MN , MNi being the masses of the heavy neutrinos the branching ratio h1 → lN is 100%. From the figure we conclude that this charged scalar would have a signature similar to the W boson with higher missing energy though. Given the order of magnitude of the production cross section this charged scalar is seemingly within reach of LHC at 14 TeV for somewhat light Z bosons. See text for more details.

V. CONCLUSIONS
We have examined bounds on the dark sector of a 331 model known as 331LHN that contains heavy neutral fermions (N a ) in its spectrum based on the current Higgs and direct dark matter detection data. The model is comprised of three scalar triplets and interestingly all of them couple to the Higgs boson. Therefore we can straightforwardly find a lower bound on the mass of these scalars by imposing the LHC constraints concerning the Higgs signal strength. In particular, we found that the Higgs signal strength requires the mass of the WIMP (φ) and the charged scalars (h ± 1 ) to be all heavier than M H /2 GeV. We have computed the abundance and scattering cross section of our WIMP as well. Combining the Higgs and dark matter date, we completely ruled out the light dark matter FIG. 8. Production cross section of the charged scalar h1 at 14 TeV at the LHC as a function of the Z and charged higgs (h + 1 ) masses, which are in GeV units. The Z mass is relevant because the Z s-channel production channel is rather important. Notice that the production cross section lies in the 10 −1 pb range. window in this model.
Additionally, since the scalar φ is enforced to be lightest particle odd by the R-parity symmetry, we automatically demand the remaining scalars to heavier than say ∼ 100 GeV. Moreover, we have computed the production cross section of the charged scalars h ± 1 at the LHC, which is driven by the Z mass, and concluded that these charged scalars might be within reach of the LHC at 14 TeV for somewhat light Z bosons as shown in Fig.7 and 8. In summary, we have brought together the Higgs data and dark matter data to rule out the light dark matter window and further discussed some LHC phenomenology.