Earth-Scattering of super-heavy 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 around 5000, for DM masses up to $10^8 \,\,\mathrm{GeV}$. A reanalysis of the longer-exposure, sub-surface CDMS-I results (published in 2002) improves the previous cross section reach by two 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 $10^6$ GeV to $10^{13}$ GeV, of particular interest for heavy DM produced gravitationally at the end of inflation.