Constraints on supersymmetric dark matter for heavy scalar superpartners

We study the constraints on neutralino dark matter in minimal low energy supersymmetry models and the case of heavy lepton and quark scalar superpartners. For values of the Higgsino and gaugino mass parameters of the order of the weak scale, direct detection experiments are already putting strong bounds on models in which the dominant interactions between the dark matter candidates and nuclei are governed by Higgs boson exchange processes, particularly for positive values of the Higgsino mass parameter $\mu$. For negative values of $\mu$, there can be destructive interference between the amplitudes associated with the exchange of the standard $CP$-even Higgs boson and the exchange of the nonstandard one. This leads to specific regions of parameter space which are consistent with the current experimental constraints and a thermal origin of the observed relic density. In this article, we study the current experimental constraints on these scenarios, as well as the future experimental probes, using a combination of direct and indirect dark matter detection and heavy Higgs and electroweakino searches at hadron colliders.

Figure 1

Spin-independent scattering cross section for fixed $\tan \beta =7$, $|\mu |=600\mathrm{GeV}$, $M_1=400\mathrm{GeV}$. The black line is for $\mu <0$, and the red line is for $\mu >0$. The blue dashed line represents the LUX 2016 constraint for $m_{\chi }=400\mathrm{GeV}$. As $M_A$ increases, the heavy Higgs becomes decoupled from the LSP, and ${\sigma }_p^{\mathrm{SI}}$ approaches an asymptotic value. Note that the asymptotic value is significantly greater for $\mu >0$ than for $\mu <0$. When experimental limits drop below the asymptotic value of the $\mu <0$ branch, an upper bound and a lower bound on $M_A$ will be present, and we are forced closer to the blind spot.

Figure 2

Lower bounds on $M_A$ due to 2016 LUX bounds for $\mu >0$, assuming the observed relic density in the whole parameter space. The value of $M_A$ is chosen to be at the minimum value allowed by the LUX bound and is indicated by the color scale. In cases where the SI cross section is not allowed for all values of $M_A$, the lower bound is marked as infinity, corresponding to the red color. The region between the white dashed lines represents the well-tempered region, with the relic densities that differ from the observed value by less than 20%. It can be seen that the well-tempered region is completely excluded. However, near the blue region, away from the well-tempered region, the correct thermal relic density may still be achieved by resonant annihilation.

Figure 3

Upper bounds on $M_A$ due to 2016 LUX bounds and projected DDMD bounds 100 times stronger than LUX, respectively ($\mu <0$), assuming the observed relic density in the whole parameter space. The value of $M_A$ is chosen to be at the maximum value allowed by these bounds and is indicated by the color scale. (Note that the color scheme differs from the previous plot such that the regions where the SI cross section is allowed as $M_A\to \infty$ are always shown in blue.) The region between the white dashed lines represents the well-tempered region. Under the strengthened bound, a much larger portion of the $|\mu |-M_1$ plane is constrained. The dashed line below corresponds to where the left-hand side of Eq. (6) is zero, corresponding to the vanishing of the neutralino coupling to the SM Higgs. Below this line, the blind spot cannot be obtained since the left-hand side of Eq. (6) becomes negative.

Figure 4

Upper bounds on $M_A$ due to 2016 LUX bounds, adjusted by the thermal WIMP relic density at each point in the plane. The strength of the LUX bound quickly decreases as one departs from the well-tempered region, since the WIMP relic density decreases quickly below the correct value. The gray region has relic density greater than 1.2 times the correct relic density, unless the neutralino mass is close to the resonant annihilation condition, $m_A=2m_{{\tilde{\chi }}_1^0}$, for which the proper relic density may be obtained and the upper bound becomes the one shown in Fig. 3.

Figure 5

Constraints on the $|\mu |\text{−}{M}_1$ plane under relic density constraints and the present and projected DDMD constraints. The well-tempered region ($\mu \simeq M_1$) naturally attains the correct relic density, while the region below may attain the correct value if $M_A$ is tuned to mediate resonant annihilation. The required value of $M_A$ is constrained by the LUX and 100 times strengthened LUX bound on the SI cross section. The blue region is allowed by the 100 times strengthened LUX bound; the blue and the green regions are allowed under current LUX bound. Note that the boundaries of the LUX constraint (red) and of the $\mathrm{LUX}/100$ constraint (green) above the blue region correspond to the boundaries in Fig. 3 where the upper bound on $M_A$ is quickly lifted to infinity. The constraints below the blue region are due to the overcompensation in the scattering cross section from the heavy Higgs contribution.

Figure 6

Thermal relic density shown in color on the $|\mu |\text{−}{M}_1$ plane for various $\tan \beta .M_A$ is taken to be at the center of blind spot (maximum cancellation). Note that $\mu$ is always negative for the blind spot to occur. The yellow region is consistent with the observed relic density. In the regions between the white dashed lines, $M_A$ can be adjusted to mediate resonant annihilation while keeping ${\sigma }_p^{\mathrm{SI}}<{10}^{-11}\mathrm{pb}$. Blind spots are not achieved in the gray area since the left-hand side of Eq. (6) becomes negative and destructive interference cannot happen. In this region, the ${\sigma }_p^{\mathrm{SI}}<{10}^{-11}\mathrm{pb}$ requirement does not set an upper bound for $M_A$ but only a lower bound, though it is still possible to tune $M_A$ to achieve resonant annihilation for $m_{\chi }$ high enough.

Figure 7

Exclusion bounds on the well-tempered region and the A-funnel region in the $\tan \beta \text{−}{M}_A$ plane. The well-tempered region is represented in the left panel, and the A-funnel region is represented in the right panel. The colored regions are excluded at 95% C.L. by the ATLAS or CMS results. The dark gray regions are not consistent with ${\sigma }_p^{\mathrm{SI}}\le {10}^{-11}\mathrm{pb}$.

Figure 8

Net exclusion status of the well-tempered region and the A-funnel region. Each data point represents a point with the proper relic density. Data points are first checked for exclusion by CMS, then by ATLAS, then by the CMS electroweakino searches (see the following section), with the color coding of each data point corresponding to the method by which it is first excluded. Values of $M_A$ are labeled next to selected data points. The sparseness of points in the A-funnel region reflects its narrowness relative to the well-tempered region, as seen in Fig. 6.

Figure 9

Plot analogous to Fig. 8 with $M_A$ chosen at the lower boundary consistent with ${\sigma }_p^{\mathrm{SI}}={10}^{-11}\mathrm{pb}$. Only exclusions from the CMS $\varphi \to \tau \tau$ search are shown.

Figure 10

Plot analogous to Fig. 8 with $M_A$ chosen at the upper limit consistent with ${\sigma }_p^{\mathrm{SI}}={10}^{-11}\mathrm{pb}$. Only exclusions from the CMS $\varphi \to \tau \tau$ search are shown.

Figure 11

Leading order cross sections for various electroweakino pair productions. Each data point corresponds to a blind spot with small $M_1$ and $|\mu |$ in the well-tempered region ($\mu \simeq M_1$) that was not excluded by the $\varphi \to \tau \tau$ searches, although one outlier is not shown for the sake of readability. The plot incorporates points from all values of $\tan \beta$, since $\tan \beta$ does not have a significant effect on $\sigma$. For these data points, $M_1\simeq |\mu |$, and changes in the sign of $|\mu |-M_1$ can occur between data points. Thus, the composition of the electroweakinos changes between data points as well. This results in bumps in the depicted curves since binolike electroweakinos have lower cross sections than Higgsino-like electroweakinos of comparable mass.

Figure 12

Branching ratios for dark matter annihilation products, including $W^{+}{W}^{-}$ (blue), $ZZ$ (green), $t\overline{t}$ (red), $b\overline{b}$ (pink), $ZH$ (yellow), $hA$ (orange), $W^{\pm }{H}^{\mp }$ (purple), and their sum (black). We see that for $m_{{\tilde{\chi }}_1^0}<200\mathrm{GeV}$ the $W^{+}{W}^{-}$, $ZZ$, and $b\overline{b}$ decay channels dominate. At $m_{{\tilde{\chi }}_1^0}\simeq 200\mathrm{GeV}$, the $t\overline{t}$ decay channel becomes prevalent but begins to diminish for large $m_{{\tilde{\chi }}_1^0}$. For $m_{{\tilde{\chi }}_1^0}>200\mathrm{GeV}$, the branching ratios for annihilation into $W^{+}{W}^{-}$ and $ZZ$ are similar, and the decays into $ZH,hA$, and $W^{\pm }{H}^{\mp }$ become significant.

Figure 13

Calculated spin-dependent cross sections for $\tan \beta =15$ (yellow dots), $\tan \beta =10$ (red dots), $\tan \beta =7$ (green dots), and $\tan \beta =5$ (blue dots). The upper branch corresponds to the well-tempered region, while the lower one corresponds to the A-funnel region. The red solid line represents the current 90% C.L. bound on the spin-dependent cross section coming from IceCube for annihilation into $WW$, and the orange line represents that for annihilation into $t\overline{t}$. The bound for annihilation into $ZZ$ is very similar to the bound for annihilation into $WW$. The magenta and dashed purple lines combine these bounds, weighting them by the branching ratios for our data, with the dashed purple line further taking into account the decays into $ZH,W^{\pm }{H}^{\mp }$, and $hA$. The bounds for decay in $b\overline{b}$ are several orders of magnitude weaker and are not shown.