Impact of form factor uncertainties on interpretations of coherent elastic neutrino-nucleus scattering data

The standard model coherent elastic neutrino-nucleus scattering (CE$\nu$NS) cross section is subject to nuclear form factor uncertainties, mainly driven by the root-mean-square radius of the neutron density distribution. Motivated by COHERENT phases I-III and future multi-ton direct detection dark matter searches, we evaluate these uncertainties in cesium iodide, germanium, xenon and argon detectors. We find that the uncertainties become relevant for momentum transfers $q\gtrsim 20$ MeV, are essentially independent of the form factor parameterization and are larger for light elements, reaching up to 11% for argon. Consequently, form factor uncertainties are not important for CE$\nu$NS induced by reactor or solar neutrinos. Taking into account these uncertainties, we then evaluate their impact on measurements of CE$\nu$NS at COHERENT, the diffuse supernova background (DSNB) neutrinos and sub-GeV atmospheric neutrinos. We show that the number of events in COHERENT involves relative uncertainties that---depending on recoil energy and nuclide---can be as large as 52%. For DSNB and atmospheric neutrino fluxes the uncertainties can reach values up to 7% and 16%, respectively. Finally, we consider their impact on searches for nonstandard neutrino interactions, sterile neutrinos and neutrino generalized interactions. We point out that studies of new physics using CE$\nu$NS data are greatly affected by neutron form factor uncertainties, which if not properly taken into account may lead to the misidentification of new physics signals. The uncertainties quantified here are also relevant for dark matter direct detection searches.