Anatomy of the inert two-Higgs-doublet model in the light of the LHC and non-LHC dark matter searches

The inert two-Higgs-doublet model (i2HDM) is a theoretically well-motivated example of a minimal consistent dark matter (DM) model which provides monojet, mono-$Z$, mono-Higgs, and vector-boson-$\mathrm{fusion}+{\mathit{E}}_{\mathrm{T}}^{\mathrm{miss}}$ signatures at the LHC, complemented by signals in direct and indirect DM search experiments. In this paper we have performed a detailed analysis of the constraints in the full five-dimensional parameter space of the i2HDM, coming from perturbativity, unitarity, electroweak precision data, Higgs data from the LHC, DM relic density, direct/indirect DM detection, and LHC monojet analysis, as well as implications of experimental LHC studies on disappearing charged tracks relevant to a high DM mass region. We demonstrate the complementarity of the above constraints and present projections for future LHC data and direct DM detection experiments to probe further i2HDM parameter space. The model is implemented into the CalcHEP and micrOMEGAs packages, which are publicly available at the HEPMDB database, and it is ready for a further exploration in the context of the LHC, relic density, and DM direct detection.

Figure 1

Restrictions on the $(m_1^2,m_2^2)$ plane coming from the requirement that the inert vacuum is the deepest minimum of the potential. The three cases correspond to (a) $R>1$, (b) $0<R<1$, (c) $-1<R<0$. Light and dark grey correspond to models with an inert $v_1=v$, $v_2=0$ and a pseudoinert $v_1=0$, $v_2=v$ vacuum, respectively, while the blue region in between corresponds to the mixed vacuum, when both $v_1$ and $v_2$ are nonzero. The dashed region in the left plot indicates coexistence of the inert and pseudoinert minima at different depths.

Figure 2

The part of the (${\lambda }_{345}$, ${\lambda }_2$) parameter space allowed by the unitarity, perturbativity, and scalar potential constraints.

Figure 3

Effect of the $S$ and $T$ constraints on the $M_{h^{+}}-M_{h_2}$ mass difference: (a) and (b) show the color map of the $S$ and $T$ parameters, respectively, in the $(M_{h^{+}},M_{h_2})$ plane; (c) shows the color map of the $M_{h^{+}}-M_{h_2}$ split in the ($S$, $T$) plane together with the 65% and 95% exclusion contours based on the ${\chi }^2$ ($S$, $T$) characterization for 2 degrees of freedom.

Figure 4

The relic density, ${\mathrm{\Omega }}_{\mathrm{DM}}{h}^2$, as a function of $M_{h_1}$ for various ${\lambda }_{345}$ parameters. The red-shaded region in the left frame is excluded by the LEP data, since in this region $W$ and $Z$ bosons would decay to the light inert scalars. The horizontal red line corresponds to the relic density upper limit given by Eq. (30).

Figure 5

Rescaled spin independent direct detection rates ${\widehat{\sigma }}_{\mathrm{SI}}$ versus $M_{h_1}$ and the LUX100 constraint. The red-shaded region in the left frame is excluded by LEP data.

Figure 6

Color maps of DM relic abundance projected on the plane $(M_{h_1},{\lambda }_{345})$. The three plots correspond to the surviving points after progressively imposing the three layers of constraints described in the text.

Figure 7

Color maps of DM relic abundance projected on the planes $(M_{h_1},M_{h_2})$ and $(M_{h_2},M_{h^{+}})$, with all the constraints imposed.

Figure 8

Projection on two planes of the scan points passing all constraints, and fitting the PLANCK relic abundance within two sigmas. We show both a wide scan with masses between 10 and 1000 GeV, and a zoom on the low mass region.

Figure 9

Feynman diagram representing effective $h^{+}\to h_1{\pi }^{+}$ via $W-\pi$ mixing.

Figure 10

The decay width of $h^{+}$ (left) as well as its lifetime together with the decay length (right).

Figure 11

The $\mathrm{\Omega }{h}^2$ value for $\mathrm{\Delta }M/M\ll 1$ and ${\lambda }_{345}$ parameter space and the $pp\to h^{+}{h}^{-}+h^{\pm }{h}_{1,2}$ production rate evaluated for the LHC@8 TeV.

Figure 12

Feynman diagrams for the $pp\to h_1{h}_{1}j$ process contributing to a monojet signature.

Figure 13

Feynman diagrams for the $q\overline{q}\to h_1{h}_{2}g$ ($gq\to h_1{h}_{2}q$) process contributing to a monojet signature.

Figure 14

Feynman diagrams for the $q\overline{q}\to h_1{h}_{1}Z$ process contributing to a mono-$Z$ signature.

Figure 15

Feynman diagrams for the $gg\to h_1{h}_{1}H$ process contributing to a mono-Higgs signature.

Figure 16

Feynman diagrams for the $q\overline{q}\to h_1{h}_{2}H$ process contributing to a mono-Higgs signature.

Figure 17

Diagrams for $qq\to q^{{(}^{\prime })}{q}^{{(}^{\prime })}{h}_1{h}_1$ DM production in the vector boson fusion process.

Figure 18

Cross sections versus dark matter mass, $M_{h_1}$, for processes contributing to monojet, mono-Z, mono-Higgs, and VBF signatures for the LHC@8 TeV and LHC@13 TeV.

Figure 19

Cross sections and 95% C.L.s for $pp\to h_1{h}_{1}j$ versus $M_{h_1}$ at 8 and 13 TeV. In both cases, the cross sections are shown for three different values of ${\lambda }_{345}$: (i) ${\lambda }_{345}=0.1$ (blue dashed curve), (ii) ${\lambda }_{345}=-0.01$ (yellow dashed curve), and (iii) the maximum ${\lambda }_{345}$ value (green dashed curve) allowed by constraints (described in text). (a) Results for 8 TeV, with limits (solid red curve) calculated using the ATLAS analysis [106]. (b) Results for 13 TeV, with projected limits for the ATLAS analysis [106] with luminosities of $20{\mathrm{fb}}^{-1}$, $100{\mathrm{fb}}^{-1}$, and $3000{\mathrm{fb}}^{-1}$ (red, magenta, and black solid lines) at 13 TeV.

Figure 20

Projected limit on ${\lambda }_{345}$ from $pp\to h_1{h}_{1}j$ at 13 TeV derived from the analysis presented in Fig. 19.

Figure 21

Cross sections and 95% C.L.s for $pp\to h_1{h}_{2}j$ versus $M_{h_1}$ at 8 and 13 TeV. In both cases, the cross sections are shown for two different values of $\mathrm{\Delta }M=M_{h_2}-M_{h_1}$: (i) $\mathrm{\Delta }M=1\mathrm{GeV}$ (blue dashed cuve), and (ii) $\mathrm{\Delta }M=100$ (yellow dashed curve). (a) Results for 8 TeV, with limits (solid red curve) calculated using the ATLAS analysis [106]. (b) Results for 13 TeV, with projected limits for the ATLAS analysis [106] with luminosities of $20{\mathrm{fb}}^{-1}$, $100{\mathrm{fb}}^{-1}$, and $3000{\mathrm{fb}}^{-1}$ (red, magenta, and black solid lines) at 13 TeV.

Figure 22

Projection of the 5D random scan of the i2HDM into the ($M_{h_1}$, ${\lambda }_{345}$) plane and the expected reach of the LHC@13 TeV with $3{\mathrm{ab}}^{-1}$ of integrated luminosity using $h_1{h}_{2}j$ and $h_1{h}_{1}j$ channels as well as for XENON1T experiment indicated by black, dark grey, and light grey colors, respectively. Excluded points are plotted on the top of the allowed points demonstrating the colored region of the parameter space which will always be allowed (AA): (a) and (b) present AA parameter space for the combined constraints for large and zoomed ($M_{h_1}$, ${\lambda }_{345}$) regions, respectively; (c) and (d) present AA regions for separate XENON1T and $h_1{h}_1+\mathrm{jet}$ LHC13 constraints, respectively.

Figure 23

Projection of the 5D random scan of the i2HDM into the ($M_{h_1}$, ${\lambda }_{345}$) plane and the expected reach of the LHC@13 TeV with $3{\mathrm{ab}}^{-1}$ of integrated luminosity using $h_1{h}_{2}j$ and $h_1{h}_{1}j$ channels as well as for the XENON1T experiment. Allowed points are on the top of the excluded ones; therefore the black and grey colors present the region which will always be excluded (AE) or probed by the above experiments.

Figure 24

Projection of the 5D random scan of the i2HDM into (a),(b) ($M_{h_1}$, $M_{h_2}$) and (c),(d) ($M_{h_2}$, $M_{h^{+}}$) planes and the expected reach of the LHC@13 TeV with $3{\mathrm{ab}}^{-1}$ of integrated luminosity using $h_1{h}_{2}j$ and $h_1{h}_{1}j$ channels as well as for the XENON1T experiment. Allowed points are on the top of the excluded ones, presenting AE points. The left panels (a),(c) present a bigger region of the parameter space, while the right ones (b),(d) present a zoomed region with AE points.

Figure 25

The 2D projections of the 5D random scan of the i2HDM satisfying all constraints (Cut-1 to Cut-4) considered above for Figs. 26 and 27 plus the lower limit on the constraint on relic density given by Eq. (30), taking into consideration the collider limits of monojet signatures at 13 TeV with $3{\mathrm{ab}}^{-1}$ of integrated luminosity and the projections of the DD XENON1T experiment. In the first row we present the parameter space of the plane ($M_{h_1},{\lambda }_{345}$) in the $\text{range}\subset [10\mathrm{GeV}–1000\mathrm{GeV}]$). In the second row we present the planes ($M_{h_1}$, ${\lambda }_{345}$) and ($M_{h_1}$, $M_{h_2}$) in the $\text{range}\subset [50\mathrm{GeV}–80\mathrm{GeV}]$).

Figure 26

Color maps of DM relic density for 2D projections of the 5D random scan of the i2HDM: each row demonstrates the effect of consequent application of the experimental and theoretical constraints in the $(M_{h_1},{\lambda }_{345})$, $(M_{h_1},M_{h_2})$, and $(M_{h_1},M_{h^{+}})$ planes. Each row corresponds to Cut-1–Cut-4, described in the text: Cut-1 for (a)–(c) [Eqs. (11)–(15)]; Cut-2 for (d)–(f) [Eqs. (19), (23), (22), (25), (26)]; Cut-3 for (g)–(i) [${\mathrm{\Omega }}_{\mathrm{DM}}^{\text{Planck}}{h}^2\le 0.1184+2\times 0.012$]; Cut-4 for (j)–(l) [LUX].

Figure 27

Color maps of DM relic density for 2D projections of the 5D random scan of the i2HDM for the parameter space restricted to (10 GeV–200 GeV) for $M_{h_1},M_{h_2}$, and $M_{h^{+}}$. As for Fig. 26 each row corresponds to Cut-1–Cut-4, described in the text: Cut-1 for (a)–(c) [Eqs. (11)–(15)]; Cut-2 for (d)–(f) [Eqs. (19), (23), (22), (25), (26)]; Cut-3 for (g)–(i) [${\mathrm{\Omega }}_{\mathrm{DM}}^{\text{Planck}}{h}^2\le 0.1184+2\times 0.012$]; Cut-4 for (j)–(l) [LUX].

Figure 28

The 2D projections of the random scan of the i2HDM for points satisfying all constraints and providing the correct relic abundance within two sigmas of the PLANCK result. The top row corresponds to the “full” parameter space $10\mathrm{GeV}<M_{h_1},M_{h_2},M_{h^{+}}<1000\mathrm{GeV}$, while the lower row refers to the “zoomed” parameter space $10\mathrm{GeV}<M_{h_1},M_{h_2},M_{h^{+}}<200\mathrm{GeV}$.