Coherent photon scattering background in sub-$\mathrm{GeV}/c^2$ direct dark matter searches

Proposed dark matter detectors with eV-scale sensitivities will detect a large background of atomic (nuclear) recoils from coherent photon scattering of MeV-scale photons. This background climbs steeply below $\sim 10\mathrm{eV}$, far exceeding the declining rate of low-energy Compton recoils. The upcoming generation of dark matter detectors will not be limited by this background, but further development of eV-scale and sub-eV detectors will require strategies, including the use of low nuclear mass target materials, to maximize dark matter sensitivity while minimizing the coherent photon scattering background.

Figure 1

Energy differential cross sections for 1460 keV photons from ${}^{40}\mathrm{K}$ decay in free silicon, germanium, and helium atoms. The low energy portion of the coherent scattering spectrum is dominated by Rayleigh scattering, while the high energy components are dominated by nuclear Thomson scattering and Delbrück scattering [6, 8]. For low recoil momenta in condensed systems, structure effects may modify the spectrum from the free atom ones shown (see text). The high energy cutoff of the coherent spectra vary with mass and photon energy as per Eq. (1). The Compton scattering spectra shown is an approximation using the Klein-Nishina formula, with cutoffs for the electron shell binding energies and the semiconductor bandgaps [4, 13, 14]. All energies are given in true recoil energy. The spectral shape expected in silicon for the elastic scattering of dark matter with $0.1\mathrm{GeV}/c^2$ mass is shown assuming a Maxwellian dark matter velocity distribution with $v_o=220\mathrm{m}/\mathrm{s}$, $v_{\mathrm{esc}}=544\mathrm{m}/\mathrm{s}$, and $v_e=244\mathrm{m}/\mathrm{s}$ [15].