Joint analysis of reactor and accelerator CE$ν$NS data on germanium: implications for the Standard Model and nuclear physics

TL;DR

The paper performs the first comprehensive joint CEνNS analysis on germanium by consolidating SNS (accelerator) data from COHERENT Ge with reactor-site measurements (CONUS+, TEXONO, νGeN), to extract fundamental SM parameters and nuclear-structure inputs. It employs a consistent cross-section framework with proton/neutron form factors and neutrino charge radii, using Helm FFs and multiple nuclear-radius inputs, and analyzes data with time- and energy-bin fits, including flux and background systematics. The results yield a low-energy weak mixing angle around $\sin^2\vartheta_W = 0.271^{+0.023}_{-0.026}$ and a neutron Ge radius around $R_n(Ge)=7.6^{+1.6}_{-1.7}$ fm, with the NSM prediction for $R_n(Ge)$ disfavored at about $2\sigma$ when combined with reactor data; neutrino charge radii remain consistent with SM in marginal analyses, though degeneracies exist that reactor inputs help to alleviate. The study underscores the power of combining reactor and accelerator CEνNS data to break parameter degeneracies and improve precision on SM and nuclear-physics quantities, and it points to flux normalization as a key systematic for resolving residual tensions and guiding future high-precision CEνNS measurements.

Abstract

This work presents the first comprehensive joint analysis of all available Coherent Elastic Neutrino-Nucleus Scattering (CE$ν$NS) data on germanium: those observed at the Spallation Neutron Source (SNS) by the COHERENT collaboration and those of the nuclear reactors revealed by the CONUS+ experiment using germanium detectors. In addition to COHERENT and CONUS+, we incorporate reactor data from TEXONO and $ν$GeN, thereby enhancing both the statistical significance and the systematic reliability of our study. We provide state-of-the-art determinations of key nuclear physics and Standard Model parameters, including the neutron root-mean-square (rms) radius of germanium nuclei, the weak mixing angle, and the neutrino charge radius. The observed tension of about $2 σ$ between the COHERENT germanium measurement and the Standard Model prediction motivates a detailed reassessment of the theoretical cross-section. In particular, we examine the impact of nuclear form factors and uncertainties in the nuclear radius, as well as the potential influence of a systematic shift in the neutrino flux normalisation at the SNS. Our results highlight the reliability of CE$ν$NS as a precision tool, reinforced by the complementarity of different experimental inputs, and lay the groundwork for future advances in the field.

Figures (7)

• Figure 1: (a) Neutron density distributions of the $^{76}$Ge nucleus obtained with the Helm model by using an average neutron rms radius $R_n^{\rm NSM}=4.22\;\rm fm$ as indicated by the NSM Hoferichter:2020osn (solid blue line) and with HF+BCS calculations obtained by using the D1M (dashed-dotted purple) or D1S (dashed orange) Gogny forces. (b) Related FFs, see Eq. (\ref{['eq:FF']}), of the neutron densities shown in panel (a). The gray area indicates the region of interest of the COHERENT germanium experiment.
• Figure 2: Marginal $\Delta\chi^2$ profile as a function of the number of CE$\nu$NS events. For comparison, the CE$\nu$NS prediction for different nuclear models is shown by the vertical lines: using a Helm neutron FF with an average neutron rms radius $R_n^{\rm NSM}=4.22\;\rm fm$ as predicted by NSM Hoferichter:2020osn (solid blue), or parameterizing the nuclear density distribution with a D1M (dashed-dotted purple) or D1S (dashed orange) Gogny type model. The light blue area indicates the systematic uncertainty on the theoretical prediction $\sigma_\eta=10.3\%$.
• Figure 3: Agreement between CE$\nu$NS data and SM predictions for COHERENT CsI+Ar (orange dashed contour), reactors (blue dotted-dashed band), COHERENT germanium (green solid contour) and the combined analysis (black region), separate for electron and muon neutrinos. Contours are shown at 90% CL, and the black point represents the best-fit, while the red cross indicates perfect agreement with the SM prediction.
• Figure 4: Constraints on the weak mixing angle at different confidence levels from the joint analysis of CsI and Ar data (dashed orange), reactors (dashed-dotted blu) and COHERENT germanium (green), the latter assuming two different parameterisations for the nuclear structure. The combined analysis is shown in black while the SM prediction is shown by the red vertical line.
• Figure 5: Constraints obtained by fitting the weak mixing angle and the average rms Ge neutron radius on COHERENT Ge data (solid green band) and reactors (dashed-dotted blue band), as well as the prior on the weak mixing angle from $\nu-e^-$ data (dashed magenta band) and the result of a combined analyis (black contour) at 1$\sigma$ CL. The upper (right) panel shows the one-dimensional marginalisation on neutron radius (weak mixing angle) from the combined analysis at different CLs. The red lines indicate the SM low-energy value of the weak mixing angle and the NSM prediction for $R_n(\rm{Ge})$.