Probing conventional and new physics at the ESS with coherent elastic neutrino-nucleus scattering

Abstract: We explore the potential of the European Spallation Source (ESS) in probing physics within and beyond the Standard Model (SM), based on future measurements of coherent elastic neutrino-nucleus scattering (CE$ν$NS). We consider two SM physics cases, namely the weak mixing angle and the nuclear radius. Regarding physics beyond the SM, we focus on neutrino generalized interactions (NGIs) and on various aspects of sterile neutrino and sterile neutral lepton phenomenology. For this, we explore the violation of lepton unitarity, active-sterile oscillations as well as interesting upscattering channels such as the sterile dipole portal and the production of sterile neutral leptons via NGIs. The projected ESS sensitivities are estimated by performing a statistical analysis considering the various CE$ν$NS detectors and expected backgrounds. We find that the enhanced statistics achievable in view of the highly intense ESS neutrino beam, will offer a drastic improvement in the current constraints obtained from existing CE$ν$NS measurements. Finally, we discuss how the ESS has the potential to provide the leading CE$ν$NS-based constraints, complementing also further experimental probes and astrophysical observations.

• The paper demonstrates ESS's capability to achieve a ±0.011 precision on sin²θW and tighter neutron rms radius limits via multi-target detector analysis.
• It employs a detailed EFT framework to assess scalar, vector, axial, and tensor non-standard interactions, outperforming previous CEνNS results in specific mass ranges.
• The study probes sterile neutrino oscillations and dipole portal scenarios, establishing ESS as a key facility for exploring conventional and new neutrino physics.

Probing Standard Model and New Physics at ESS Using Coherent Elastic Neutrino-Nucleus Scattering

Introduction: ESS as a High-Statistics CE$\nu$NS Facility

This study examines the sensitivity of the European Spallation Source (ESS) to both Standard Model (SM) and beyond-the-Standard-Model (BSM) phenomena via coherent elastic neutrino-nucleus scattering (CE$\nu$NS). Leveraging the intense neutrino flux generated by the ESS's superconducting proton accelerator, the work quantifies the expected event yields and evaluates projected constraints for various detectors employing CsI, Xe, Ge, Si, Ar, and $\mathrm{C_3F_8}$ nuclear targets. Both classic SM tests—such as precision measurement of the weak mixing angle and neutron rms radius—and diverse BSM physics scenarios including neutrino generalized interactions (NGIs), sterile neutrino/neutral lepton production, and lepton unitarity violation are systematically addressed.

CE$\nu$NS Formalism and Detector Modeling

The underlying physics is formulated by reviewing the coherent SM cross section at tree level, mediated by $Z$ exchange and proportional to the square of the neutron number, with nuclear form factors parametrized via the Helm model. The analysis incorporates both vector and suppressed axial-vector SM contributions, accounting for target-specific nuclear spin dependencies. For new physics probes, a model-independent effective field theory approach is adopted, capturing all Lorentz-invariant four-fermion operators relevant for NGI: scalar (S), pseudoscalar (P), vector (V), axial-vector (A), and tensor (T). The study evaluates both light and heavy mediator cases, parameterizing interaction strengths through generic couplings and masses.

The simulation pipeline utilizes detailed detector specifications—mass, threshold, resolution, and backgrounds—derived from available ESS proposals. Signal and background rates are statistically treated using Poisson $\chi^2$ fits, and spectral smearing is incorporated via energy-dependent Gaussian functions. Flat systematic uncertainties of 10% for signal and 1% for background are imposed following prior experimental guidance.

SM Parameter Projections: Weak Mixing Angle and Neutron RMS Radius

A principal focus is the low-energy determination of $\sin^2 \theta_W$, a benchmark electroweak parameter. The combined ESS analysis yields a projected $1\sigma$ uncertainty on $\sin^2 \theta_W$ of $\pm 0.011$, representing substantial improvement over current CE$\nu$NS-based limits (e.g., $\sim$60% tighter than COHERENT and 80% over Dresden-II). The ESS detectors' statistical power and diversified nuclear targets enable robust cross-verification of SM predictions and complement high-precision atomic parity violation (APV) results.

Figure 1: Projected sensitivity on the weak mixing angle from the combined analysis of the proposed ESS detectors.

The neutron rms radius ($R_n$), poorly constrained especially for non-lead isotopes, is analyzed for each target. The expected $1\sigma$ ranges for $R_n$ show marked improvement over existing constraints, with ESS projected to tighten CsI limits by $\sim$40% and provide first-time sensitivity for Si and $\mathrm{C_3F_8}$. Simultaneous fitting of $\sin^2 \theta_W$ and $R_n$ reveals weak parameter correlations except for heavy nuclei, where form factor effects at low recoil energies become more pronounced.

Figure 2: Projected sensitivity on the neutron rms radii of different detectors at the ESS.

NGI Sensitivities: Scalar, Vector, Axial-Vector, and Tensor Channels

ESS CE$\nu$NS is shown to be competitive or leading for constraining NGIs in specific parameter spaces. Combined ESS detector analysis projects competitive 90% C.L. sensitivity contours for scalar and vector interactions, especially in the $M_S > 40~$MeV and $25 < M_V < 200~$MeV ranges, outperforming bounds from existing CE$\nu$NS (COHERENT), elastic $\nu$-$e$ scattering, dark matter experiments, beam-dump, collider, and astrophysical supernova data. Axial-vector and tensor channels, being nuclear-spin suppressed, are less competitive against electron-scattering-derived limits, although ESS provides the strongest CE$\nu$NS-only constraints.

Figure 3: Projected sensitivities at 90% C.L. for the various $X=\{S,V,A,T\}$ interactions in a combined detector analysis.

Probing Sterile Neutrino and Neutral Lepton Phenomenology

The study systematically addresses CE$\nu$NS sensitivity to sterile neutrino oscillations, lepton unitarity violation (through parameters $\alpha_{11}, \alpha_{22}$), electromagnetic upscattering (“sterile dipole portal”), and production of massive sterile neutral leptons via various NGIs.

Lepton unitarity violation: CE$\nu$NS is insensitive to $\alpha_{11}$ but retains moderate sensitivity to $\alpha_{22}$, projecting $1-\alpha_{22}^2 < 0.14$ at 90% C.L.; oscillation experiments remain dominant.

Figure 4: Projected sensitivity on the NU parameter $\alpha_{22}$.

Sterile oscillations: ESS CE$\nu$NS can probe active-sterile mixing in the $(\sin^2{2\theta_{14}}, \Delta m^2)$ and $(\sin^2{2\theta_{24}}, \Delta m^2)$ planes, but the sensitivity is limited compared to dedicated short-baseline experiments.

Figure 5: Projected 90% C.L. sensitivity regions for sterile neutrino oscillations.

Sterile dipole portal: By leveraging upscattering with transition magnetic moments (TMMs), ESS excludes $\mu_{\nu_e}$ ($\mu_{\nu_\mu}$) down to $8\times10^{-10}\,\mu_B$ ($6\times10^{-10}\,\mu_B$) for sub-10 MeV SNL masses, improving COHERENT bounds by a factor of five and extending reach up to 50 MeV SNL masses—a regime unprobed by reactors or current solar/DM experiments.

Figure 6: Projected 90% C.L. sensitivity on the sterile dipole portal scenario in $(m_{N_R}, \mu_{\nu_e/\mu})$.

NGI-mediated SNL production: For the upscattering scenario with Lorentz-invariant scalar, vector, axial-vector, or tensor mediation, ESS matches or exceeds current XENONnT and COHERENT sensitivity for mediator/SNL masses above a few MeV. DUNE Near Detector measurements will outperform ESS for SNL masses above $\sim$50 MeV owing to higher-energy fluxes and improved nuclear spin coverage.

Discussion: Interplay, Complementarity, and Future Prospects

The combined-multitarget ESS strategy enables both cross-checks and global fits of SM parameters, essential for reducing model/systematic uncertainties in nuclear and weak interactions. For BSM physics, CE$\nu$NS at ESS will provide a critical complement to reactor, solar, and accelerator-based searches. The ability to test light, weakly-coupled mediators and massive SNL scenarios in previously inaccessible regimes is notable.

These improvements are not solely technical; the refined constraints can inform model building (e.g., UV completions with light/hidden sector mediators, sterile neutrino mass models) and have relevance for astrophysical phenomena—such as SN1987A cooling and BBN dynamics—via feedback on $N_\mathrm{eff}$, supernova energy loss rates, and lepton-number violation effects.

Conclusion

ESS's high-intensity neutrino flux and multiple advanced detector concepts will significantly extend precision low-energy neutrino physics. The projected improvements in $\sin^2 \theta_W$ and $R_n$ measurements, and competitive exclusion regions for NGI, sterile neutrino oscillations, and SNL production, establish ESS CE$\nu$NS as a leading probe of both conventional and novel interactions. The multitarget paradigm, robust statistical methods, and diverse physics case studies suggest that ESS will play a central role in next-generation neutrino and weak sector physics, bridging gaps between nuclear, accelerator, and cosmology-based experiments.