Not as big as a barn: Upper bounds on dark matter-nucleus cross sections

Abstract

Critical probes of dark matter come from tests of its elastic scattering with nuclei. The results are typically assumed to be model independent, meaning that the form of the potential need not be specified and that the cross sections on different nuclear targets can be simply related to the cross section on nucleons. For pointlike spin-independent scattering, the assumed scaling relation is σ χA ∝ A 2 μ 2 A σ χN ∝ A 4 σ χN , where the A 2 comes from coherence and the μ 2 A ≃ A 2 m 2 N from kinematics for m χ ≫ m A. Here we calculate where model independence ends, i.e., where the cross section becomes so large that it violates its defining assumptions. We show that the assumed scaling relations generically fail for dark matter-nucleus cross sections σ χA ∼ 10 −32-10 −27 cm 2 , significantly below the geometric sizes of nuclei and well within the regime probed by underground detectors. Last, we show on theoretical grounds, and in light of existing limits on light mediators, that pointlike dark matter cannot have σ χN ≳ 10 −25 cm 2 , above which many claimed constraints originate from cosmology and astrophysics. The most viable way to have such large cross sections is composite dark matter, which introduces significant additional model dependence through the choice of form factor. All prior limits on dark matter with cross sections σ χN > 10 −32 cm 2 with m χ ≳ 1 GeV must therefore be reevaluated and reinterpreted.

Terrestrial and martian heat flow limits on dark matter

“…Finally, we note that in a number of recent publications [15,31,33], it has been pointed out that the spin-independent DM-nucleon scattering cross section as presented in Eq. ( 6), reaches a theoretical transition point at σ χN ≈ 10 −26 cm 2 .…”

Direct detection and complementary constraints for sub-GeV dark matter

“…As a rough indication of how large cross sections are in principle possible, we also show in each case the parameter range where the couplings are well inside the perturbative regime (for a more detailed treatment, see ref. [89]). Right panel.…”

Present and future status of light dark matter models from cosmic-ray electron upscattering

“…One may worry that these cross sections are so large that they exceed the perturbativity bounds. Although this can be a concern in some cases [51], we show in the Appendix that the couplings here remain fully perturbative.…”