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A consistent neutrino determination of the low-energy weak mixing angle

This paper presents a consistent reanalysis of low-energy neutrino scattering data, combining coherent elastic neutrino-nucleus and neutrino-electron scattering measurements to determine the low-energy weak mixing angle as $\sin^2\theta_W^{\rm low}(\nu\,\text{data}) = 0.233^{+0.007}_{-0.006}$ , thereby providing an independent precision test of the Standard Model that complements atomic parity violation results.

Original authors: M. Atzori Corona, M. Cadeddu, N. Cargioli, F. Dordei, L. Ferro, C. Giunti, R. Pavarani, M. Sestu

Published 2026-10-23

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Original authors: M. Atzori Corona, M. Cadeddu, N. Cargioli, F. Dordei, L. Ferro, C. Giunti, R. Pavarani, M. Sestu

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The universe is held together by a set of fundamental rules, much like the laws of physics that govern how a ball falls or how a star burns. Among these rules is a specific number, a value that helps physicists understand how particles interact through the weak nuclear force, one of the four fundamental forces of nature. This number, known as the weak mixing angle, acts like a dial that determines the strength of these interactions. Just as the dial on a radio changes the station, this angle changes depending on the energy level at which it is measured. At very high energies, such as those found in the heart of a star or a particle collider, the value is one thing. But at the low energies we experience in everyday life, the value settles into a specific, predictable range. Verifying that this value matches the prediction is a crucial test of our current understanding of the universe, known as the Standard Model. If the number is slightly off, it could mean there are new, undiscovered particles or forces at play.

For decades, scientists have tried to pin down this low-energy value with extreme precision. One of the most successful methods has involved studying atoms, specifically cesium, to see how they behave when their internal symmetry is slightly broken by the weak force. This technique, called atomic parity violation, has provided a very sharp measurement, but it relies heavily on complex calculations of how electrons move around the nucleus. Because these calculations are so intricate, there is always a lingering question: could the result be skewed by a tiny error in the math rather than a flaw in the physics? To answer this, a team of researchers decided to try a completely different approach. Instead of looking at atoms, they looked at neutrinos, the ghostly particles that pass through everything almost without interacting.

The researchers gathered a vast collection of data from experiments where neutrinos bounced off other particles. They focused on two specific types of interactions. In the first, a neutrino hits an entire atomic nucleus and causes it to recoil, a process that is sensitive to the number of neutrons inside the atom. In the second, a neutrino hits a single electron directly. By combining the results from dozens of experiments using different sources of neutrinos—from nuclear reactors to particle accelerators and even the sun—the team was able to calculate the weak mixing angle without ever needing to rely on the complex atomic calculations used in the cesium studies. They treated the data from each experiment with a consistent set of rules, carefully accounting for the uncertainties in how many neutrinos were produced and how the detectors responded.

The result of this massive data synthesis is a new, independent measurement of the weak mixing angle at low energy. The team found a value of 0.233, with a small margin of error that places the true value between 0.227 and 0.240. This number sits comfortably within the range predicted by the Standard Model and aligns well with the previous measurements taken from cesium atoms. While the new measurement is not yet as precise as the atomic one, its importance lies in its independence. It confirms that the value derived from atoms is not an artifact of complex theoretical math but a real feature of nature. The agreement between these two very different methods—one based on the structure of atoms and the other on the scattering of ghostly particles—strengthens the case that our current model of the universe is correct.

The researchers also looked ahead, noting that the precision of this neutrino-based measurement is expected to improve significantly. Future experiments are already being planned to reduce the uncertainties in how neutrino beams are measured and how detectors respond to them. As these new data come in, the gap between the neutrino measurement and the atomic measurement will likely close. If they continue to agree, it will provide a robust validation of the Standard Model. If they eventually disagree, it would be a clear signal that new physics is waiting to be discovered. For now, the work stands as a successful, independent check of a fundamental constant, proving that we can measure the universe's rules in more than one way and still get the same answer.

Technical Summary: A Consistent Neutrino Determination of the Low-Energy Weak Mixing Angle

Problem Statement
The weak mixing angle, $\sin^2 \theta_W$ , is a fundamental parameter of the Standard Model (SM) of electroweak interactions. While its value is well-constrained at high energies, its behavior at low momentum transfer is a sensitive probe of the theory's quantum structure. At low energies, the SM prediction approaches a well-defined plateau. Currently, the most precise determination of this low-energy value comes from Atomic Parity Violation (APV) in cesium. However, the extraction of $\sin^2 \theta_W$ from APV relies heavily on complex atomic-structure calculations and nuclear inputs (such as the neutron skin thickness), which have historically shifted the inferred value as theoretical models improved. This creates a need for an independent determination based on different experimental techniques and theoretical uncertainties to robustly test the SM's predicted running of the weak mixing angle.

Methodology
The authors perform a global analysis of low-energy neutrino scattering data to derive a neutrino-only determination of $\sin^2 \theta_W$ . The methodology involves:

Re-evaluation of APV: The paper first updates the APV determination in cesium. This includes incorporating recent atomic and nuclear inputs, specifically refining the "neutron-skin" correction using proton-cesium elastic scattering data ( $R_n = 4.94 \pm 0.21$ fm) and updated electron wave functions solved via the Dirac-Hartree-Fock-Slater equations. Two values are reported based on different atomic calculations (Ref. [13] and Ref. [25]), with the former adopted as the primary benchmark ( $\sin^2 \theta_W^{\text{low}}(\text{APV}) = 0.2348 \pm 0.0022$ ).
Global Neutrino Fit: The authors consistently reanalyze a broad set of existing low-energy neutrino scattering datasets within a common electroweak framework. This framework accounts for electroweak radiative corrections and relevant theoretical uncertainties. The datasets include:
- Coherent Elastic Neutrino-Nucleus Scattering (CE $\nu$ NS): Data from COHERENT (CsI, Argon, Germanium), CONUS+, TEXONO, and nuclear recoil data from dark matter detectors (XENONnT, PandaX-4T, LZ).
- Neutrino-Electron Scattering ( $\nu$ ES): Data from reactor experiments (TEXONO), accelerator experiments (LSND, LAMPF, BNL-E734, CHARM-II), and solar neutrino interactions in dark matter detectors.
Statistical Combination: Individual $\chi^2$ profiles are constructed for each dataset, incorporating experimental uncertainties (flux, detector response, backgrounds, quenching factors) and nuisance parameters. These profiles are summed to generate a global $\chi^2$ profile for the combined neutrino data, preserving asymmetric uncertainties.

Key Contributions

Independent Benchmark: The paper establishes a determination of the low-energy weak mixing angle derived solely from neutrino scattering, independent of the atomic-structure calculations required for APV.
Unified Framework: It provides a consistent reanalysis of diverse neutrino datasets (reactor, accelerator, solar, and dark matter sources) using a single electroweak framework, updating older measurements where previous determinations relied on outdated theoretical inputs.
Complementarity Analysis: The work explicitly highlights the complementary nature of CE $\nu$ NS and $\nu$ ES. While CE $\nu$ NS is sensitive to the nuclear weak charge (dominated by neutrons), $\nu$ ES probes electron couplings without nuclear structure uncertainties. Their combination allows for a robust extraction of $\sin^2 \theta_W$ .

Results
The global analysis of all available neutrino data yields the following value for the low-energy weak mixing angle in the $\overline{\text{MS}}$ scheme at zero momentum transfer:
$\sin^2 \theta_W^{\text{low}}(\nu \text{ data}) = 0.233^{+0.007}_{-0.006}$

Comparison with SM: This result is compatible with the SM prediction for the low-energy plateau ( $\sin^2 \theta_W^{\text{SM, low}} = 0.23873(5)$ ).
Comparison with APV: The neutrino result is consistent with the updated APV determination ( $0.2348 \pm 0.0022$ ) but currently has a larger uncertainty (approximately three times that of the APV result).
Process Breakdown: The analysis shows that $\nu$ ES data currently provide a more precise constraint than CE $\nu$ NS data alone, though both are compatible with the SM and each other.

Significance and Claims
The paper claims that its primary significance lies not in surpassing the precision of APV, but in providing an independent test of the Standard Model at low momentum transfer.

Validation of SM Running: The agreement between the neutrino-based determination and the APV result (despite their vastly different theoretical systematics) provides a non-trivial validation of the SM's predicted running of the weak mixing angle.
Robustness Against Theory Shifts: Given the historical evolution of the APV value due to improvements in atomic theory, the neutrino determination serves as a crucial cross-check. It helps distinguish whether future deviations from the SM are due to new physics or specific to the theoretical interpretation of a particular observable.
Future Prospects: The authors note that while current precision is limited by experimental systematics (particularly neutrino flux normalization in accelerator experiments and detector response in reactor experiments), future CE $\nu$ NS experiments (e.g., with in-situ flux normalization) and improved $\nu$ ES measurements are expected to close the precision gap with APV. A future agreement between independent neutrino and atomic determinations at comparable precision would constitute a stringent validation of the electroweak sector.

Technical Summary: A Consistent Neutrino Determination of the Low-Energy Weak Mixing Angle

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