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

Searches in final states with two leptons plus missing transverse energy, targeting supersymmetric particles or invisible decays of the Higgs boson, were performed during Run 1 of the LHC. Recasting the results of these analyses in the context of the Inert Doublet Model (IDM) using MadAnalysis 5, we show that they provide constraints on inert scalars that significantly extend previous limits from LEP. Moreover, these LHC constraints allow to test the IDM in the limit of very small Higgs-inert scalar coupling, where the constraints from direct detection of dark matter and the invisible Higgs width vanish. PACS numbers: 12.60.-i, 12.60.Fr The Inert Doublet Model is one of the simplest extensions of the Standard Model (SM). First introduced as a toy model for electroweak (EW) symmetry breaking studies [1], it was later found to potentially improve naturalness [2], be compatible with Coleman-Weinberg EW symmetry breaking (EWSB) [3] as well as accommodate dark matter (DM) through different potential mechanisms [2, 4-6] and with interesting signatures [7-11]. It can moreover explain EW baryogenesis [12, 13], neutrino masses [14], can be constrained from LEP measurements [15] and predicts a rich phenomenology at the LHC [2, 16-21]. The discovery of a Higgs-like particle with a mass of about 125 GeV at the LHC [22, 23] has already made a tremendous impact on the phenomenology of the IDM, dramatically reducing its available parameter space [24]. Besides its interplay with Higgs phenomenology, the IDM can yield interesting signals at the LHC, involving in particular two [17], three [18] or multiple [19] leptons along with missing transverse energy, E miss T. Such signals have so far been studied in the literature only as predictions and never as constraints from existing LHC results. In this work we show that existing data on + − + E miss T searches from the 8 TeV LHC run -performed by the experimental collaborations with supersymmetry (SUSY) or invisible Higgs decays in mind -begin to provide significant constraints on the IDM parameter space that are highly complementary to those obtained from DM observables.Let us begin by briefly presenting the IDM and setting some useful notations for the subsequent analysis. In the IDM, the SM is extended by the addition of a second scalar, Φ, transforming as a doublet under SU (2) L . This doublet Φ is odd under a new discrete Z 2 symmetry, whereas all other fields are even. In Feynman gauge we can write the two scalar doublets aswhere v = √ 2 0|H|0 ≈ 246 GeV denotes the vacuum expectation value of the neutral component of H. The h state corresponds to the physical SM-like Higgs boson, whereas G 0 and G ± are the Goldstone bosons. The "inert" sector consists of a neutral CP-even scalar H 0 , a pseudo-scalar A 0 , and a pair of charged scalars H ± . The scalar potential of the model readsThe masses and interactions of the scalar sector are fixed by the scalar-potential parameters λ 1...5 and µ 2 , which can be traded for the physically more intuitive setwhere the Higgs and inert scal...