Dark Matter that Interacts with Baryons: Experimental Limits on the Interaction Cross-section for 27 Atomic Nuclei, and Resultant Constraints on the Particle Properties

Abstract: To constrain the properties of dark matter (DM) that interacts with nucleons, we have conducted an experimental search for any anomalous heating of ordinary baryonic matter at 77 K. Our tabletop experiment is motivated by the possibility (discussed in a previous paper) that DM particles with masses in the $\sim 1 - 2 m_{\rm p}$ range could be captured by and concentrated within the Earth. For suitable parameters, this phenomenon could lead to a substantial density $\sim 10^{14}\,\rm cm^{-3}$ of thermalized (300 K) DM particles at Earth's surface that would heat cooler baryonic matter. Our experiment involves precise differential measurements of the evaporation rate of liquid nitrogen in a storage dewar within which various materials are immersed. The results revealed no statistically-significant detections of heating in the 27 elements with molar fractions $> 10^{-5}$ in Earth's crust. For material with the average composition of Earth's crust, our measurements imply a $3 \sigma$ upper limit of $1.32 \times 10^{-27}\, n_{\rm 14}^{-1} (m_{\rm DM}/2\,m_{\rm p})^{-1/2}\,\rm cm^2$ on the mean cross-section for scattering with thermal HIDM at 300 K, where $10^{14}\,n_{14} \, \rm cm^{-3}$ is the particle density at Earth's surface. In combination with a lower limit on the scattering cross-section, obtained from a consideration of the heat flow through the Earth's crust (Neufeld, Farrar & McKee 2018), our experiment places an upper limit of $1.6 \times 10^{13}\,\rm cm^{-3}$ on the density of DM at the Earth's surface. This in turn, significantly constrains the properties for any DM candidate that interacts with baryons.