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

TL;DR

This paper evaluates how high-precision neutrino scattering data can be used to accurately determine neutron distributions in nuclei, analyzing theoretical uncertainties and proposing methods to improve measurement accuracy.

Contribution

It compares form factor parametrizations and decompositions for extracting neutron distributions, quantifies uncertainties, and demonstrates potential precision improvements with future experiments.

Findings

Form factor approaches enable ~15% accuracy in neutron radius extraction.

Reducing backgrounds could achieve ~1% precision in measurements.

Theoretical uncertainties significantly impact the interpretation of high-precision data.

Abstract

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.