Status of the inert doublet model and the role of multileptons at the LHC

A feature of the inert doublet model (IDM) is to provide a dark matter candidate together with an alteration of both direct and indirect collider constraints that allow for a heavy Higgs boson. We study the IDM in light of recent results from Higgs searches at the Large Hadron Collider (LHC) in combination with dark matter direct detection limits from the XENON experiment. We ask under what conditions the IDM can still accommodate a heavy Higgs boson. We find that IDM scenarios with a Higgs boson in the mass range 160–600 GeV are ruled out only when all experimental constraints are combined. For models explaining only a fraction of the dark matter the limits are weakened, and IDMs with a heavy Higgs are allowed. We discuss the prospects for future detection of such IDM scenarios in the four-lepton plus missing energy channel at the LHC. This signal can show up in the first year of running at $\sqrt{s}=14\mathrm{TeV}$, and we present detector-level studies for a few benchmark models.

Figure 1

Direct detection signal for IDMs in agreement with WMAP data. The crosses represent IDM models that pass all our imposed constraints from Sec. 3 (not including LHC constraints). The upper 95% C.L. bounds from XENON-100 [53] and XENON-10 [52] are shown by the solid lines. The points labeled A1-C4 show the scattering cross section for our benchmark models. As explained in Sec. 6, the B models can only pass the constraints after taking systematic uncertainties into account, and the C models account only for a fraction of the DM density.

Figure 2

Left: The solid lines show, for different $H^0$ masses, the lowest limits on the Higgs production rates $\sigma /{\sigma }_{\mathrm{S}M}$ that the IDM can have at the LHC and still be compatible with XENON-100 data. These limits correspond to when none of the produced IDM states contribute to a signal in the LHC’s Higgs boson searches, i.e., $\mathcal{R}={\mathcal{R}}^{\mathrm{cons}}$. The constraint from a thermal freeze-out calculation of $H^0$ has not been applied yet, and $H^0$ is assumed to make up the local DM density. All other constraints, EWPT and LEP limits in particular, are taken into account. The dark (blue) region is excluded by the current Higgs search results from the LHC. Thus, only the white regions above the lines remain allowed in the IDM. Right: All lines assume an $H^0$ mass of 70 GeV. The upper (red) line assumes that $H^0$ particles provide all the local DM, the dark (blue) line below is after systematic uncertainties (see text) are included to diminish the direct detection constraints, while the lower (green) line applies when assuming that $H^0$ contribute only 10% to the local DM density.

Figure 3

All the points correspond to IDMs giving rise to a DM relic density in agreement with WMAP. Small (grey) points represent models that neither pass the LHC Higgs searches nor XENON-100 constraints, diamonds (in blue) represent models that pass LHC, and large (green) points represent models that pass XENON-100 constraint individually. Squares (in red) represent models that pass the constraints from both the LHC and XENON-100 experiments. All the other constraints of Sec. 3 have also been taken into account.

Figure 4

Feynman diagrams contributing to $pp\to 4l+{\mathrm{E̸}}_T$ in the IDM.

Figure 5

Cross sections $\sigma$ into four or more leptons from $H^{+}{H}^{-}$ and $H^{\pm }{A}^0$ production via gauge bosons (in units of 10 logarithms of $\sigma$ in fb). Here $m_{H^0}=70\mathrm{GeV}$. This contribution to the cross section is independent of the Higgs mass.

Figure 6

Cross sections $\sigma$ into four or more leptons from $A^0{A}^0$ and $H^{+}{H}^{-}$ production via the Higgs scalar $h$ (in units of 10-logarithms of $\sigma$ in fb). In this plot $m_{H^0}=70\mathrm{GeV}$, ${\mu }_2^2=0$, and $m_{H^{\pm }}=220\mathrm{GeV}$. Only Higgs production via gluon fusion is included.

Figure 7

Top left: Missing transverse energy distributions in events with four isolated leptons. Top right: The invariant mass of SF-OS lepton pairs after the cut on ${\mathrm{E̸}}_T$ has been applied. Bottom left: Distribution of $b$ tagged jets, after the cut on ${\mathrm{E̸}}_T$ and $Z$ veto. Bottom right: Invariant mass distribution for the SF-OS lepton pair producing the minimal such value per event, after all other cuts have been performed. The shaded grey regions indicate the cuts on each quantity.

Figure 8

Fine-tuning $\Delta$, without RG effects, as a function of the SM Higgs mass. IDMs are represented by dark (red) marks for the benchmark models and light (green) ones for models in the scan. The SM, given a cutoff scale of 1.5 TeV, is represented by the (blue) solid line. The circles show the result for IDMs using Eq. (a4) and the crosses the result using Eq. (a5). The thick part of the solid (blue) line corresponds to the remaining Higgs mass window allowed within the SM. The dashed (blue) line is the SM result with RG running of the couplings included.

Figure 9

The running of IDM parameters with energy scale $Q$ for one of our benchmark models (IDM-B1). Where the curves flatten out at around 150 TeV is when we terminate the calculation because the perturbativity limit of at least one ${\lambda }_i>4\pi$ is reached. The $m_{H^0}^2$ and ${\mu }_i^2$ curves are normalized into units of their values $m_{H^0,0}^2$, ${\mu }_{i,0}^2$ at the scale $Q=m_h$.

Figure 10

Fine-tuning measures, with RG effects included, for one of our benchmark models (IDM-B1). The notation for the plot legend is that ${\Delta }_i^X={\Delta }_{{\Lambda }_i^2}^X$, and $\sqrt{\sum _i{\Delta }_i^2}=\overline{\Delta }$ (as defined in the text).