  Recent measurements of the germanium quenching factor deviate significantly
from the predictions of the standard Lindhard model for nuclear recoil energies
below a keV. This departure may be explained by the Migdal effect in neutron
scattering on germanium. We show that the Migdal effect on the quenching factor
can mimic the signal of a light Z' or light scalar mediator in coherent elastic
neutrino nucleus scattering experiments with reactor antineutrinos. It is
imperative that the quenching factor of nuclei with low recoil energy
thresholds be precisely measured close to threshold to avoid such confusion.
This will also help in experimental searches of light dark matter.
