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_χ ≳10⁵  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 10⁸  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 10¹⁵  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 10⁶  GeV to 10¹³  GeV, of particular interest for heavy DM produced gravitationally at the end of inflation.