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

## TL;DR

This paper assesses how uncertainties in nuclear form factors affect the interpretation of coherent elastic neutrino-nucleus scattering data, with implications for neutrino physics and dark matter searches.

## Contribution

It quantifies form factor uncertainties across various detectors and evaluates their impact on neutrino measurements and new physics searches.

## Key findings

- Uncertainties become significant at momentum transfers above 20 MeV.
- Form factor uncertainties are negligible for reactor and solar neutrinos.
- Event rate uncertainties can exceed 5% for DSNB and atmospheric neutrinos.

## Abstract

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 and are essentially independent of the form factor parameterization. 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 also calculate the relative uncertainties in the number of COHERENT events for different nuclei as a function of recoil energy. For DSNB and atmospheric neutrinos, event rates at a liquid argon detector can be uncertain to more than 5%. Finally, we consider the impact of form factor uncertainties 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 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.