Combined analysis of effective Higgs portal dark matter models

We combine and extend the analyses of effective scalar, vector, Majorana and Dirac fermion Higgs portal models of dark matter (DM), in which DM couples to the Standard Model (SM) Higgs boson via an operator of the form ${\mathcal{O}}_{\mathrm{DM}}{H}^{†}H$. For the fermion models, we take an admixture of scalar $\overline{\psi }\psi$ and pseudoscalar $\overline{\psi }i{\gamma }_5\psi$ interaction terms. For each model, we apply constraints on the parameter space based on the Planck measured DM relic density and the LHC limits on the Higgs invisible branching ratio. For the first time, we perform a consistent study of the indirect detection prospects for these models based on the WMAP7/Planck observations of the cosmic microwave background, a combined analysis of 15 dwarf spheroidal galaxies by Fermi-LAT and the upcoming Cherenkov Telescope Array (CTA). We also perform a correct treatment of the momentum-dependent direct search cross section that arises from the pseudoscalar interaction term in the fermionic DM theories. We find, in line with previous studies, that current and future direct search experiments such as LUX and XENON1T can exclude much of the parameter space, and we demonstrate that a joint observation in both indirect and direct searches is possible for high mass weakly interacting massive particles. In the case of a pure pseudoscalar interaction of a fermionic DM candidate, future gamma-ray searches are the only class of experiment capable of probing the high mass range of the theory.

Figure 1

Figures adopted with permission from Ref. [92]. Left: The “signal” and “background” regions of interest (RoIs) used in the ring method of Ref. [97]. Right: Separation of the signal and background RoIs into 28 sub-RoIs for the morphological analysis of Ref. [92].

Figure 2

Contours of fixed scalar relic density for $f_{\text{rel}}=1$ (black solid), 0.1 (red dashed) and 0.01 (blue dotted). The grey shaded region is excluded due to an overabundance of dark matter. Left: A close-up of the resonantly enhanced annihilation region, $m_S\sim m_h/2$. Larger values of ${\lambda }_{hS}$ are excluded by an upper limit of 19% (pink solid) at $2\sigma$ C.L. or 5% (pink dotted) at $1\sigma$ C.L. on $\mathcal{BR}(h\to SS)$. Right: Relic density contours for the full range of $m_S$.

Figure 3

Indirect search limits on the scalar model parameter space. The grey and pink shaded regions are excluded respectively by the observed DM relic density and an upper limit of 19% on $\mathcal{BR}(h\to SS)$ at $2\sigma$ C.L. Values of ${\lambda }_{hS}$ below the current $1\sigma$ C.L. (brown solid) curve are excluded at more than $1\sigma$ C.L. Regions below the future 90% C.L. curve with the Einasto (blue dashed) and contracted NFW (brown dotted) profile will be excluded. Left: A close-up of the resonantly enhanced annihilation region, $m_S\sim m_h/2$. Right: The full range of $m_S$.

Figure 4

Direct search limits on the scalar model parameter space. The grey shaded region is ruled out by the observed DM relic density. Regions excluded by the LUX (XENON1T) experiment are delineated with blue dashed (blue dotted) curves and dark (light) shadings. Left: A close-up of the resonantly enhanced annihilation region, $m_S\sim m_h/2$. The pink shaded region is excluded by an upper limit of 19% on $\mathcal{BR}(h\to SS)$ at $2\sigma$ C.L. Right: The full range of $m_S$.

Figure 5

Contours of fixed vector relic density for $f_{\text{rel}}=1$ (black solid), 0.1 (red dashed) and 0.01 (blue dotted). The grey shaded region is excluded due to an overabundance of dark matter. Left: A close-up of the resonantly enhanced annihilation region, $m_V\sim m_h/2$. Larger values of ${\lambda }_{hV}$ are excluded by an upper limit of 19% (pink solid) at $2\sigma$ C.L. or 5% (pink dotted) at $1\sigma$ C.L. on $\mathcal{BR}(h\to VV)$. Right: Relic density contours for the full range of $m_V$.

Figure 6

Indirect search limits on the vector model parameter space. The grey and pink shaded regions are excluded respectively by the observed DM relic density and an upper limit of 19% on $\mathcal{BR}(h\to VV)$ at $2\sigma$ C.L. Values of ${\lambda }_{hV}$ below the current $1\sigma$ C.L. (brown solid) curve are excluded at more than $1\sigma$ C.L. Regions below the future 90% C.L. curve with the Einasto (blue dashed) and contracted NFW (brown dotted) profile will be excluded. Left: A close-up of the resonantly enhanced annihilation region, $m_V\sim m_h/2$. Right: The full range of $m_V$.

Figure 7

Direct search limits on the vector model parameter space. The grey shaded region is ruled out by the observed relic density of dark matter. Regions excluded by the LUX (XENON1T) experiment are delineated with blue dashed (blue dotted) curves and dark (light) shadings. Left: A close-up of the resonantly enhanced annihilation region, $m_V\sim m_h/2$. The pink shaded region is excluded by an upper limit of 19% on $\mathcal{BR}(h\to VV)$ at $2\sigma$ C.L. Right: The full range of $m_V$.

Figure 8

Contours of fixed Majorana relic density for $f_{\text{rel}}=1$ (black solid), 0.1 (red dashed) and 0.01 (blue dotted). The grey shaded region is ruled out due to an overabundance of dark matter. The green shaded region is where the EFT approximation of the full theory breaks down for ${\lambda }_{h\chi }/{\mathrm{\Lambda }}_{\chi }>4\pi /2m_{\chi }$. Left: A close-up of the resonantly enhanced annihilation region, $m_{\chi }\sim m_h/2$. Larger values of ${\lambda }_{h\chi }/{\mathrm{\Lambda }}_{\chi }$ are excluded by an upper limit of 19% (pink solid) at $2\sigma$ C.L. or 5% (pink dotted) at $1\sigma$ C.L. on $\mathcal{BR}(h\to \overline{\chi }\chi )$. Right: Relic density contours for the full range of $m_{\chi }$.

Figure 9

Indirect search limits on the Majorana model parameter space. The grey and pink shaded regions are excluded respectively by the relic density and the Higgs invisible width constraints. The green shaded region is where the EFT approximation of the full theory breaks down for ${\lambda }_{h\chi }/{\mathrm{\Lambda }}_{\chi }>4\pi /2m_{\chi }$. Values of ${\lambda }_{h\chi }/{\mathrm{\Lambda }}_{\chi }$ below the current $1\sigma$ C.L. (brown solid) curve are excluded at more than $1\sigma$ C.L. Regions below the future 90% C.L. curve with the Einasto (blue dashed) and contracted NFW (brown dotted) profiles will be excluded. Left: A close-up of the resonantly enhanced annihilation region, $m_{\chi }\sim m_h/2$. Right: The full range of $m_{\chi }$.

Figure 10

Breakdown of the current $1\sigma$ C.L. (blue solid) in the Majorana fermion parameter space when $\cos \xi =0$. The grey shaded region is excluded by the relic density constraint. The green shaded region is where the EFT approximation of the full theory breaks down for ${\lambda }_{h\chi }/{\mathrm{\Lambda }}_{\chi }>4\pi /2m_{\chi }$. Contributions to the combined current $1\sigma$ C.L. come from WMAP 7-year observations of the CMB (green solid) and a combined analysis of 15 dwarf galaxies using 6 years of the Fermi-LAT data (red dashed). Left: A close-up of the resonantly enhanced annihilation region, $m_{\chi }\sim m_h/2$. Right: The full range of $m_{\chi }$.

Figure 11

Breakdown of the future 90% C.L. (Einasto) in the Majorana fermion parameter space when $\cos \xi =0$ (blue solid). The grey shaded region is excluded by the relic density constraint. The green shaded region is where the EFT approximation of the full theory breaks down for ${\lambda }_{h\chi }/{\mathrm{\Lambda }}_{\chi }>4\pi /2m_{\chi }$. Contributions to the combined future 90% C.L. (Einasto) come from the Planck polarization data (green solid), projected improvements in Fermi-LAT sensitivity towards observation of a further 15 southern dwarf galaxies over 10 years (red dashed) and projected limits from the CTA using the Einasto profile (orange dotted). Left: A close-up of the resonantly enhanced annihilation region, $m_{\chi }\sim m_h/2$. Right: The full range of $m_{\chi }$.

Figure 12

Breakdown of the future 90% C.L. (NFW, $\gamma =1.3$) in the Majorana fermion parameter space when $\cos \xi =0$ (blue solid). The grey shaded region is excluded by the relic density constraint. The green shaded region is where the EFT approximation of the full theory breaks down for ${\lambda }_{h\chi }/{\mathrm{\Lambda }}_{\chi }>4\pi /2m_{\chi }$. Contributions to the combined future 90% C.L. (NFW, $\gamma =1.3$) come from the Planck polarization data (green solid), projected improvements in Fermi-LAT sensitivity towards observation of a further 15 southern dwarf galaxies over 10 years (red dashed) and projected limits from the CTA experiment using the contracted NFW ($\gamma =1.3$) profile (orange dotted). Left: A close of the resonantly enhanced annihilation region, $m_{\chi }\sim m_h/2$. Right: The full range of $m_{\chi }$.

Figure 13

Direct search limits on the Majorana model parameter space. The grey shaded region is ruled out by the relic density constraint. Regions excluded by the LUX (XENON1T) experiment are delineated with blue dashed (blue dotted) curves and dark (light) shadings. Although EFTs are valid at direct search experiments, our scaling of the LUX/XENON1T limits by the relic abundance parameter $f_{\text{rel}}={\mathrm{\Omega }}_{\chi }/{\mathrm{\Omega }}_{\mathrm{DM}}$ introduces a sensitivity to UV corrections when the EFT approximation in DM annihilations breaks down for ${\lambda }_{h\chi }/{\mathrm{\Lambda }}_{\chi }>4\pi /2m_{\chi }$. Left: A close-up of the resonantly enhanced annihilation region, $m_{\chi }\sim m_h/2$. The pink shaded region is excluded by an upper limit of 19% on $\mathcal{BR}(h\to \overline{\chi }\chi )$ at $2\sigma$ C.L. Right: The full range of $m_{\chi }$.

Figure 14

Contours of fixed Dirac relic density for $f_{\text{rel}}=1$ (black solid), 0.1 (red dashed) and 0.01 (blue dotted). The grey shaded region is ruled out due to an overabundance of dark matter. The green shaded region is where the EFT approximation of the full theory breaks down for ${\lambda }_{h\psi }/{\mathrm{\Lambda }}_{\psi }>4\pi /2m_{\psi }$. Left: A close-up of the resonantly enhanced annihilation region, $m_{\psi }\sim m_h/2$. Larger values of ${\lambda }_{h\psi }/{\mathrm{\Lambda }}_{\psi }$ are excluded by an upper limit of 19% (pink solid) at $2\sigma$ C.L. or 5% (pink dotted) at $1\sigma$ C.L. on $\mathcal{BR}(h\to \overline{\psi }\psi )$. Right: Relic density contours for the full range of $m_{\psi }$.

Figure 15

Indirect search limits on the Dirac model parameter space. The grey and pink shaded regions are excluded respectively by the relic density and the Higgs invisible width constraints. The green shaded region is where the EFT approximation of the full theory breaks down for ${\lambda }_{h\psi }/{\mathrm{\Lambda }}_{\psi }>4\pi /2m_{\psi }$. Values of ${\lambda }_{h\psi }/{\mathrm{\Lambda }}_{\psi }$ below the current $1\sigma$ C.L. (brown solid) curve are excluded at more than $1\sigma$ C.L. Regions below the future 90% C.L. curve with the Einasto (blue dashed) and contracted NFW (brown dotted) profile will be excluded. Left: A close-up of the resonantly enhanced annihilation region, $m_{\psi }\sim m_h/2$. Right: The full range of $m_{\psi }$.

Figure 16

Direct search limits on the Dirac model parameter space. The grey shaded region is ruled out by the relic density constraint. The regions excluded by the LUX (XENON1T) experiment are delineated with blue dashed (blue dotted) curves and dark (light) shadings. Although EFTs are valid at direct search experiments, our scaling of the LUX/XENON1T limits by the relic abundance parameter $f_{\text{rel}}={\mathrm{\Omega }}_{\psi }/{\mathrm{\Omega }}_{\mathrm{DM}}$ introduces a sensitivity to UV corrections when the EFT approximation in DM annihilations breaks down for ${\lambda }_{h\psi }/{\mathrm{\Lambda }}_{\psi }>4\pi /2m_{\psi }$. Left: A close-up of the resonantly enhanced annihilation region, $m_{\psi }\sim m_h/2$. The pink shaded region is excluded by an upper limit of 19% on $\mathcal{BR}(h\to \overline{\psi }\psi )$ at $2\sigma$ C.L. Right: The full range of $m_{\psi }$.