Prospect of the NUCLEUS Experiment at Chooz for Coherent Elastic Neutrino-Nucleus Scattering and New Physics Searches

The NUCLEUS experiment aims to measure coherent elastic neutrino-nucleus scattering (CE$ν$NS) at unprecedentedly low nuclear recoil energies using gram-scale cryogenic calorimeters operated at the Chooz nuclear power plant in France. Access to recoil energies at the $\mathcal{O}(10~\mathrm{eV})$ scale enables CE$ν$NS studies at extremely low momentum transfer and provides enhanced sensitivity to new physics. In this work, we present sensitivity projections for the upcoming NUCLEUS technical and physics runs, incorporating a data-driven treatment of the low-energy excess (LEE) observed during commissioning. We develop a likelihood framework that exploits reactor-power variation to disentangle signal and background in a low signal-to-background regime and to assess the impact of the dominant systematic uncertainties. For the Technical Run with a 7 g CaWO$_4$ target, we find competitive sensitivity to several scenarios beyond the Standard Model, which do not require a CE$ν$NS observation. For the Physics Run, assuming complete suppression of the LEE, we project a 4.7 $σ$ observation of CE$ν$NS with a statistical precision of about 20 % in 1 year, enabling a determination of the weak mixing angle at the lowest momentum transfer probed to date with CE$ν$NS and leading CE$ν$NS-based constraints on the neutrino charge radius and new mediator models.