Electron ionization via dark matter-electron scattering and the Migdal effect
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Abstract
There are currently several existing and proposed experiments designed to\nprobe sub-GeV dark matter (DM) using electron ionization in various materials.\nThe projected signal rates for these experiments assume that this ionization\nyield arises only from DM scattering directly off electron targets, ignoring\nsecondary ionization contributions from DM scattering off nuclear targets. We\ninvestigate the validity of this assumption and show that if sub-GeV DM couples\nwith comparable strength to both protons and electrons, as would be the case\nfor a dark photon mediator, the ionization signal from atomic scattering via\nthe Migdal effect scales with the atomic number $Z$ and 3-momentum transfer\n$\\mathbf{q}$ as $Z^2 \\mathbf{q}^2$. The result is that the Migdal effect is\nalways subdominant to electron scattering when the mediator is light, but that\nMigdal-induced ionization can dominate over electron scattering for heavy\nmediators and DM masses in the hundreds of MeV range. We put these two\nionization processes on identical theoretical footing, address some theoretical\nuncertainties in the choice of atomic wavefunctions used to compute rates, and\ndiscuss the implications for DM scenarios where the Migdal process dominates,\nincluding for XENON10, XENON100, and the recent XENON1T results on light DM\nscattering.\n