Response of CsI[Na] to Nuclear Recoils: Impact on Coherent Elastic Neutrino-Nucleus Scattering (CE$ u$NS)

A new measurement of the quenching factor for low-energy nuclear recoils in CsI[Na] is presented. Past measurements are revisited, identifying and correcting several systematic effects. The resulting global data are well-described by a physics-based model for the generation of scintillation by ions in this material, in agreement with phenomenological considerations. The uncertainty in the new model is reduced by a factor of four with respect to an energy-independent quenching factor initially adopted as a compromise by the COHERENT collaboration. A significantly improved agreement with Standard Model predictions for the first measurement of CE$ u$NS is generated. We emphasize the critical impact of the quenching factor on the search for new physics via CE$ u$NS experiments.