Earth scattering of superheavy dark matter: Updated constraints from detectors old and new

Direct searches for dark matter (DM) are continuously improving, probing down to lower and lower DM-nucleon interaction cross sections. For strongly interacting massive particle (SIMP) dark matter, however, the accessible cross section is bounded from above due to the stopping effect of the atmosphere, Earth, and detector shielding. We present a careful calculation of the SIMP signal rate, focusing on super-heavy DM ($m_{\chi }\gtrsim {10}^5\mathrm{GeV}$) for which the standard nuclear-stopping formalism is applicable, and provide code for implementing this calculation numerically. With recent results from the low-threshold CRESST 2017 surface run, we improve the maximum cross section reach of direct detection searches by a factor of about 5000, for DM masses up to $10^8\mathrm{GeV}$. A reanalysis of the longer-exposure, subsurface CDMS-I results (published in 2002) improves the previous cross section reach by 2 orders of magnitude, for masses up to $10^{15}\mathrm{GeV}$. Along with complementary constraints from SIMP capture and annihilation in the Earth and Sun, these improved limits from direct nuclear scattering searches close a number of windows in the SIMP parameter space in the mass range $10^6\mathrm{GeV}$ to $10^{13}\mathrm{GeV}$, of particular interest for heavy DM produced gravitationally at the end of inflation.

Figure 1

Average direction of incoming dark matter flux at the SUF. The average direction is described by the angle $\gamma$ defined in Eq. (3) and the surrounding text. The shaded blue band shows the maximum and minimum values over the course of the year while the zoomed inset shows the daily variation due to the Earth’s rotation.

Figure 2

Example of mapping the initial speed of DM particles to the final speed at the detector. The dashed line denotes the DM speed at the top of the atmosphere, and solid lines denote the final DM speed after propagation through the atmosphere (blue line), then after propagation through the Earth (green line), and then after propagation through the shielding (orange line). In this example, we assume DM particles traveling vertically downwards. Left: Detector at MPI at a depth of $\sim 30\mathrm{cm}$ (CRESST 2017 surface run). Right: Detector at SUF at a depth of 10.6 m (CDMS-I). Note the different cross sections in the two cases. The shaded green band in the right panel corresponds to a 4% uncertainty on the depth of the detector (roughly equivalent to a $3\sigma$ fluctuation on the number of underground scatters).

Figure 3

Final speed distribution at an underground detector at SUF. Final speed distribution for DM particles of mass $10^5\mathrm{GeV}$ at a detector at the SUF after propagation through the atmosphere, Earth, and lead shielding. The dashed black lines show the unperturbed Maxwell-Boltzmann speed distribution. Speeds in the grey shaded region are typically too small to excite a nuclear recoil of energy 10 keV, the analysis threshold for CDMS-I. The speed distribution is shown as a function of the direction of the average DM flux (for fixed cross section). The different curves (from top to bottom) show results for equally spaced $\gamma$ values from $\gamma =180°$ (average flux from overhead) to $\gamma =0°$ (average flux from below).

Figure 4

Final speed distribution at different detector locations for a range of DM-nucleon cross sections. Final speed distribution for DM particles of mass $10^5\mathrm{GeV}$ at a detector at the MPI (left) and SUF (right) after propagation through the atmosphere, Earth, and shielding. The dashed black lines show the unperturbed Maxwell-Boltzmann speed distribution. Speeds in the grey shaded region are (on average) too small to excite a nuclear recoil above threshold in the corresponding detector. Note the different cross section values in the two panels.

Figure 5

Constraints on strongly interacting dark matter from nuclear scattering search experiments. The orange shaded region is excluded by high-altitude experiments such as RSS [61], XQC [62, 63], IMP $7/8$ [64], IMAX [65], and SKYLAB [66] (collected in Ref. [41]). The grey shaded regions are excluded by previous analyses of direct detection experiments. This region is bounded from below by constraints from Xenon1T [3] and from the left by CRESST-III [5] and the CRESST 2017 surface run [6, 30]. The solid black line denotes the previous cross section reach from Ref. [37] (reported in Ref. [41]). The shaded blue area shows the additional region of parameter space excluded by the present reanalysis of the CDMS-I (SUF) limits [45, 46], while the shaded red region shows the new limits from the CRESST 2017 surface run [6]. We also exclude the area below the dashed blue and red lines, though we note that all constraints on SIMPs in this mass range come with caveats, as discussed in the text.

Figure 6

Summary of constraints on strongly interacting dark matter. The solid grey region shows constraints from surface and underground direct detection experiments, including the updated limits derived in this work. The orange region (dashed line) is excluded by high-altitude experiments, as in Fig. 5. Complementary constraints from IceCube (red, dotted line) [42], Earth’s heat flux (cyan, dot-dashed line) [41, 67], and DM-cosmic ray interactions (green, solid line) [71] are also shown. Note that these complementary constraints are model dependent and typically require further assumptions about dark matter, beyond its nucleon scattering cross section (e.g. self-annihilation into Standard Model states). Large areas of the SIMP dark matter parameter space are ruled out by at least two constraints, both direct searches for DM-nuclear scattering and indirect constraints.

Figure 7

Coordinate system for Earth scattering. Illustration of the coordinate system used to calculate the impact of DM scattering in the Earth. The incoming direction of a single DM particle toward the detector is denoted by $\mathbf{v}$, while the direction of the mean DM flux is denoted $⟨{\mathbf{v}}_{\chi }⟩=-{\mathbf{v}}_{\mathrm{lab}}(t)$. In the associated text, we give expressions for the DM path length to the detector and the velocity distribution in this coordinate system.