Neutrinos as background and signal in searches using the Migdal effect

Ionization or excitation resulting from the noninstantaneous response of the electron cloud to nuclear recoil is known as the Migdal effect. Dark matter searches utilizing this process set the most stringent bounds on the spin-independent dark matter-nucleon scattering cross section over a large region of the sub-GeV dark matter parameter space, underscoring its significance in dark matter detection. In this paper, we quantify the regions of dark matter parameter space that are challenging to probe via the Migdal effect due to the presence of dominant solar neutrino backgrounds for both liquid noble and semiconductor targets. Our findings reveal that there is no hard floor in the dark matter parameter space. Instead, we map the so-called neutrino fog. In mapping the neutrino fog, we identify the importance of incorporating the Migdal effect induced by neutrinos, as well as neutrino-electron scattering and dominant coherent neutrino-nucleus scattering, particularly for semiconductor targets. Furthermore, we demonstrate that a large portion of the relic density allowed parameter space lies within the neutrino fog. Finally, we estimate the exposure required to detect neutrino-induced Migdal events in direct detection experiments.