Abstract
There are currently several existing and proposed experiments designed to probe sub-GeV dark matter (DM) using electron ionization in various materials. The projected signal rates for these experiments assume that this ionization yield arises only from DM scattering directly off electron targets, ignoring secondary ionization contributions from DM scattering off nuclear targets. We investigate the validity of this assumption and show that if sub-GeV DM couples with comparable strength to both protons and electrons, as would be the case for a dark photon mediator, the ionization signal from atomic scattering via the Migdal effect scales with the atomic number $Z$ and 3-momentum transfer $\mathbf{q}$ as $Z^2 \mathbf{q}^2$. The result is that the Migdal effect is always subdominant to electron scattering when the mediator is light, but that Migdal-induced ionization can dominate over electron scattering for heavy mediators and DM masses in the hundreds of MeV range. We put these two ionization processes on identical theoretical footing, address some theoretical uncertainties in the choice of atomic wavefunctions used to compute rates, and discuss the implications for DM scenarios where the Migdal process dominates, including for XENON10, XENON100, and the recent XENON1T results on light DM scattering.
Highlights
The evidence for dark matter (DM) is overwhelming, its microscopic properties remain unknown and motivate various experimental techniques to uncover its possible nongravitational interactions [1]
The main result of this paper is the following: in models where sub-GeV DM couples comparably to electrons and protons, the ratio of the differential ionization rate dRM=dq due to the Migdal effect to the corresponding direct electron scattering rate dRe=dq satisfies dRM =dq dRe=dq
Due to these competing effects, the Migdal scattering rate in heavy atoms such as Xe is generically dominated by the largest kinematically permitted momentum transfers, typically hundreds of keV, which are small on nuclear scales but large on electron scales; by contrast, direct DMelectron scattering is dominated by the smallest momentum transfers
Summary
The evidence for dark matter (DM) is overwhelming, its microscopic properties remain unknown and motivate various experimental techniques to uncover its possible nongravitational interactions [1]. The scattering probability in the latter case is enhanced by Z2 due to coherent scattering off the nucleus, and simultaneously suppressed by the small electron mass compared to the heavy nucleus, though this suppression is mitigated somewhat when the momentum transfer to the atom is large Due to these competing effects, the Migdal scattering rate in heavy atoms such as Xe is generically dominated by the largest kinematically permitted momentum transfers, typically hundreds of keV, which are small on nuclear scales but large on electron scales; by contrast, direct DMelectron scattering is dominated by the smallest momentum transfers. Our limits presented here should be considered provisional pending a dedicated analysis of relativistic and electron correlation effects in heavy atomic systems
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