Extraction of neutron density distributions from high-statistics coherent elastic neutrino-nucleus scattering data

Forthcoming fixed-target coherent elastic neutrino-nucleus scattering experiments aim at measurements with $\cal{O}(\text{tonne})$-scale detectors and substantially reduced systematic and statistical uncertainties. With such high quality data, the extraction of point-neutron distributions mean-square radii requires a better understanding of possible theoretical uncertainties. We quantify the impact of single-nucleon electromagnetic mean-square radii on the weak-charge form factor and compare results from weak-charge form factor parametrizations and weak-charge form factor decompositions in terms of elastic vector proton and neutron form factors, including nucleon form factors $Q$-dependent terms up to order $Q^2$. We assess as well the differences arising from results derived using weak-charge form factor decompositions in terms of elastic vector proton and neutron form factors and a model-independent approach based solely on the assumption of spherically symmetric nuclear ground state. We demonstrate the impact of the main effects by assuming pseudo-data from a one-tonne LAr detector and find that, among the effects and under the assumptions considered in this paper, weak-charge form factor parametrizations and weak-charge form factor decompositions in terms of elastic vector proton and neutron form factors enable the extraction of the $^{40}\text{Ar}$ point-neutron distribution mean-square radius with a $\sim 15\%$ accuracy. With a substantial reduction of the beam-related neutron and steady-state backgrounds a $\sim 1\%$ precision extraction seems feasible, using either of the two approaches.