A Comprehensive Effective Field Theory Framework for Coherent Elastic Neutrino-Nucleus Scattering

TL;DR

This work develops a complete end-to-end EFT framework for coherent elastic neutrino-nucleus scattering (CE$\nu$NS), spanning the UV to nuclear scales. It combines low-energy LEFT operators up to dimension 8 with their QCD RG running, matches them to the chiral Lagrangian via a systematic spurion approach, and performs a detailed power-counting analysis of nuclear responses, including coherent enhancements. The framework also links LEFT to SMEFT via full tree-level UV completions, enabling a top-down interpretation of CE$\nu$NS signals in terms of NP scales and neutrino NSI parameters. By leveraging data from COHERENT, CONUS+, PandaX-4T, and XENONnT, the paper derives robust constraints on EFT operator scales and NSI parameters, while outlining a path for future refinements with expanded datasets and lattice QCD inputs. Overall, it provides a unified, theory-driven pipeline to translate CE$\nu$NS measurements into quantitative bounds on new physics across energy scales.

Abstract

Coherent elastic neutrino-nucleus scattering (CE$ν$NS) stands out as a pivotal process for precision tests of the Standard Model electroweak sector, investigations of neutrino properties, and searches for new physics (NP). Recent experimental measurements by COHERENT, CONUS+, and ton-scale xenon detectors--including PandaX-4T and XENONnT--underscore the need for a systematic theoretical framework to bridge high-energy physics scenarios with low-energy observational data. In this work, we develop a comprehensive end-to-end effective field theory (EFT) framework for CE$ν$NS, encompassing the complete energy scale hierarchy spanning the ultraviolet (UV) regime down to the nuclear sector. We consider the low-energy EFT (LEFT) operators up to dimension 8, incorporating their QCD renormalization group running effects, and employ the systematic spurion method to achieve the matching between these operators and the chiral Lagrangian. A full power counting analysis is performed, extending to nuclear response functions, which evaluates contributions from LEFT operators up to dimension 8 while accounting for the nucleon number enhancement effect intrinsic to CE$ν$NS. Moreover, we match the relevant LEFT operators for CE$ν$NS onto operators up to dimension 8 within the Standard Model EFT. By also providing their complete tree-level ultraviolet completions, this procedure establishes a consistent top-down theoretical workflow. Leveraging a broad suite of CE$ν$NS experimental data, this framework enables a combined analysis to extract constraints on the scales of EFT operators and neutrino non-standard interaction parameters.

Figures (7)

• Figure 1: Effective field theory approach to evaluate the cross section of CE$\nu$NS.
• Figure 2: Diagrams (a) and (b) show the leading-order one-body current contributions. Diagrams (c) and (d) show loop corrections to the one-body current. Diagram (e) shows the two-body current contribution.
• Figure 3: For CE$\nu$NS processes initiated by an electron-flavor neutrino, we present lower bounds at $90\%$ C.L. on the effective scale $\Lambda$ (in GeV) associated with individual LEFT Wilson coefficients $\hat{\mathcal{C}}_1^{5}$, $\hat{\mathcal{C}}_a^{6u}$, $\hat{\mathcal{C}}_a^{6d}$, $\hat{\mathcal{C}}_a^{7u}$, $\hat{\mathcal{C}}_a^{7d}$, $\hat{\mathcal{C}}_6^{7}$, $\hat{\mathcal{C}}_7^{7}$, $\hat{\mathcal{C}}_a^{8u}$, $\hat{\mathcal{C}}_a^{8d}$ and $\hat{\mathcal{C}}_9^{8}$. The limits are obtained by turning on one operator at a time. The orange, blue and green bars correspond to constraints from CONUS+, COHERENT (CsI and Ar combination), PandaX-4T and XENONnT combination, respectively.
• Figure 4: The $90\%$ C.L. allowed regions in the $(\epsilon_{ee}^{uV},\,\epsilon_{ee}^{dV})$ plane derived from the CONUS+ (orange) and COHERENT (blue) CE$\nu$NS measurements, together with the combined constraint from the PandaX-4T + XENONnT (green) solar-$^8$B analysis.
• Figure 5: Contributions to $\mathcal{O}_{ld}$ from the UV completions with $S_{12}$ , $V_1$ and $V_7$ particles.