Electroweak Constraints on Nuclear Neutron Distributions and the Low-Energy Weak Mixing Angle

Abstract

Coherent elastic neutrino--nucleus scattering (CE$ν$NS) offers a low-energy probe of the weak mixing angle, $\sin^2θ_W$, and possible new physics in the neutrino sector. Its reliable interpretation, however, requires independent constraints on the neutron distributions of the target nuclei. We exploit correlations across nuclei within an extended Skyrme energy-density-functional framework to propagate constraints from the CREX and PREX-II parity-violating electron-scattering (PVES) measurements to CE$ν$NS targets. This yields neutron form factors and radii, with relative radius uncertainties below $1\%$. Using these inferred neutron form factors, we jointly analyze the COHERENT CsI, Ge, and Ar data and obtain $\sin^2θ_W=0.231^{+0.016}_{-0.015}$, consistent with the Standard Model prediction. These results provide the first electroweak-experimentally constrained benchmarks for nuclear-structure studies, neutrino-sector electroweak tests, and CE$ν$NS signal predictions in dark-matter detectors.