# Dark Matter and 125 Gev Higgs for Idm

\addressUniversity of Warsaw, Faculty of Physics,

Hoża 69, 00-681 Warsaw, Poland

We discuss a scalar Dark Matter candidate from the Inert Doublet Model in light of discovery of a 125 GeV SM-like Higgs boson at the LHC. We explore the possibility of using the recent and future data from LHC experiments, namely the Higgs diphoton decay measurements, to constrain the properties of Dark Matter particles.

## 1 Introduction

According to the standard cosmological model around 25% of the Universe is made of cold, non-baryonic, neutral and very weakly interacting particles. The Inert Doublet Model (IDM) is one of the simplest extensions of the Standard Model (SM) that can provide such Dark Matter (DM) candidate. The scalar sector in the IDM is extended with respect to the SM-like Higgs doublet by a second doublet, , which is odd under a symmetry: .[1, 2]

The IDM can provide a viable DM candidate in agreement with collider constraints and relic density measurements in three regions of DM mass: , and .[3] Further constraints for the DM candidate can come from direct and indirect detection experiments. However, as for now there is no agreement how to consistently interpret various reported signals and the exclusion limits.[4]

In this work we set constraints on scalar DM from the IDM by using the LHC Higgs data and WMAP relic density measurements. Combining the data for the SM-like Higgs with the WMAP results excludes a large part of the IDM parameter space, setting limits on DM that are stronger or comparable to these obtained by the DM detection experiments.

## 2 The Inert Doublet Model

The IDM is defined as a 2HDM with a -symmetric potential and vacuum state:

(1) |

In the IDM only one doublet, , is involved in the EW symmetry breaking. It provides a SM-like Higgs boson , which has tree-level couplings to fermions and gauge bosons like in the SM with possible deviation from the SM in loop couplings. The second doublet, , is inert and contains four dark scalars , that have no couplings to fermions. The lightest particle coming from this doublet is stable, being a good DM candidate.

The IDM can be described by the masses of scalar particles and their physical couplings: is related to and vertices, while gives and : . Parameters of the IDM are constrained by various theoretical and experimental conditions. In our analysis we use vacuum stability constraints, that ensure the potential is bounded from below. We also demand, that the state (1) is the global, and not just a local minimum.[5, 6] Parameters of the potential should also fulfill perturbative unitarity bounds.[7]

The value of the Higgs boson mass, , and above conditions provide the following constraints for the parameters of the potential: .[8]

Masses of dark particles are constrained by the LEP measurements and EWPT to be: with an excluded region where simultaneously .[9]

## 3 The diphoton decay rate in the IDM

is the ratio of the diphoton decay rate of the Higgs particle observed at the LHC to the SM prediction. The current measured values of are for ATLAS and for CMS.[10, 11] They are in 2 agreement with the SM value , however a deviation from that value is still possible and would be an indication of physics beyond the SM.

The ratio in the IDM is given by:

(2) |

where are the total decay widths of in the SM and the IDM, while are the respective partial decay widths for . In the IDM two sources of deviation from are possible. First is a contribution to the partial decay width:[12, 13]

(3) |

where is the SM amplitude and is the contribution. The interference between and can be either constructive or destructive. The second source of deviations are possible invisible decays , which can strongly augment the total decay width with respect to the SM case. If can decay invisibly then is always below 1.[14, 13] For (and ) the invisible channels are closed, and is possible. depends only on the masses of the dark scalars and (or ), so setting a lower bound on leads to upper and lower bounds on as functions of .[15]

### decay channels open

In this region, the invisible decay channels have stronger influence on the value of than the contribution from loop.[14] If we demand that , we get allowed values of that are small, typically in range . For the allowed values of are smaller than for . The condition strongly limits the allowed parameter space of the IDM. The allowed mass difference is GeV, and values of are smaller than in the previous cases. Requesting larger leads to the exclusion of the whole region of masses, apart from .[15]

### decay channel closed

When the decay channel is closed, the values of do not depend on the value of , while the charged scalar contribution becomes more relevant. If then an exact value of is not crucial for the obtained limits on , and allowed values of are of order . For the obtained bounds are different for GeV and 120 GeV. Smaller leads to stronger limits, requiring , while larger allow . Larger value of leads to smaller allowed values of . In the case of a large region of DM masses is excluded, as it is not possible to obtain the requested value of for any value of if .[15]

### Invisible decay channels closed

If , the invisible channels are closed and the only modification to comes from the charged scalar loop (3). Enhancement in is possible when .[13, 14] Unitarity and positivity limits on and constrain the allowed values of and for a given value of . For masses of GeV are excluded, and if this bound is stronger, forbidding GeV. Also, even a small deviation from requires a relatively large , if the mass difference is of the order GeV. Small values of are preferred if is small.[15]

## 4 Combining and relic density constraints on DM

Here we compare the limits on the parameter obtained from with those coming from the requirement that the DM relic density is in agreement with the WMAP measurements: . If this condition is fulfilled, then constitutes 100% of DM in the Universe. Values of are allowed if is a subdominant DM candidate.

### Low DM mass

In the IDM the low DM mass region corresponds to masses of below 10 GeV, while the other dark scalars are heavier, GeV. To obtain the proper relic density, the coupling has to be large, for example for CDMS-II favoured mass GeV. The coupling allowed by , i.e. , is an order of magnitude smaller than needed for and thus we can conclude that the low DM mass region cannot be accommodated in the IDM with recent LHC results.

### Medium DM mass: invisible decay channels open

We first consider a case with GeV and . Red bound in the left panel of figure 1 denotes the WMAP-allowed range of . If we consider as a subdominant DM candidate with then also the regions below and above red bounds in figure 1 are allowed. This usually corresponds to larger values of . For a large portion of the parameter space limits for from , even for the least stringent case , cannot be reconciled with the WMAP-allowed region, where , excluding .

### Medium DM mass: invisible decay channels closed

Here we choose GeV and varying between and GeV. Figure 1 (central panel) gives the WMAP-allowed range with the corresponding values of . The absolute values of that lead to the proper relic density are in general larger than in the case of . From figure 1 it can be seen that this region of is consistent with , and that and constraints cannot be fulfilled for the middle DM mass region. If the IDM is the source of all DM in the Universe and GeV then the maximal value of is around . A subdominant DM candidate, which corresponds to larger , is consistent with .

### Heavy DM mass: almost degenerated particle spectra

In this case it is possible to get and be with agreement with WMAP, as shown in right panel in figure 1 for GeV and , although deviation from is very small.

## 5 Summary

The DM candidate from the IDM is consistent with the WMAP results on the DM relic density and in three regions of masses it can explain 100 % of the DM in the Universe. In a large part of the parameter space it can also be considered as a subdominant DM candidate. Measurements of the diphoton ratio done at the LHC set strong limits on masses of the DM and other dark scalars, and their self-couplings.

We can exclude the low DM mass region in the IDM, i.e. GeV, as values of needed for the proper are an order of magnitude larger than those allowed by assuming that . In the medium mass region favours degenerated and . When the mass difference is large, GeV, then values of that provide are bigger than those allowed by WMAP. We conclude it is not possible to have and all DM in the Universe explained by the IDM in the medium DM mass region. If then may be a subdominant DM candidate. If then GeV can explain 100% of DM in the Universe. For heavy DM particles it is possible to obtain and fulfill WMAP bounds, although deviation from is small.

## Acknowledgments

This work was supported in part by the grant NCN OPUS 2012/05/B/ST2/03306 (2012-2016).

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