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A LENS on DUNE-PRISM: Characterizing a Neutrino Beam with Off-Axis Measurements

This paper introduces the LENS technique, which utilizes off-axis neutrino beam measurements to independently constrain meson flux models and subsequently improve the precision of far-detector flux predictions for long-baseline oscillation experiments.

Original authors: Julia Gehrlein, Joachim Kopp, Margot MacMahon, George A. Parker

Published 2026-09-16

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CC BY 4.0

Original authors: Julia Gehrlein, Joachim Kopp, Margot MacMahon, George A. Parker

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

Neutrinos are the most abundant massive particles in the universe, yet they are also the most elusive. They zip through ordinary matter—passing through the Earth, the Sun, and even our own bodies—without ever leaving a trace. To catch them, scientists build enormous detectors deep underground, waiting for the rare moment a neutrino strikes an atom and creates a flash of light. The goal of modern neutrino physics is to understand how these particles change their identity as they travel, a process called oscillation. By measuring these changes with extreme precision, researchers hope to uncover secrets about the fundamental laws of the universe, such as why there is more matter than antimatter. However, as experiments have grown larger and more sensitive, the biggest obstacle is no longer a lack of data, but a lack of certainty about the starting point. Scientists must know exactly what kind of neutrino beam they are sending and how it behaves before it even reaches the detector, but predicting this beam is incredibly difficult because it depends on complex interactions between protons and atomic nuclei that are not perfectly understood.

A major upcoming experiment, the Deep Underground Neutrino Experiment, or DUNE, plans to send a powerful beam of neutrinos from Fermilab in Illinois to a massive detector in South Dakota. To ensure the measurements are accurate, the experiment includes a "near detector" located just a few hundred meters from the source. This near detector is designed to measure the beam before the neutrinos have had a chance to change. A clever strategy called PRISM allows this near detector to move sideways, off the direct centerline of the beam. Because the energy of the neutrinos changes depending on the angle at which they are viewed, taking measurements from different positions provides a rich set of data. The standard approach uses these off-axis measurements to create a prediction of what the beam will look like when it arrives at the far detector, effectively canceling out many errors. However, this method still relies on a theoretical model of how the beam is created, and if that model is slightly wrong, the prediction will be flawed.

In a new study, researchers Julia Gehrlein, Joachim Kopp, Margot MacMahon, and George A. Parker propose a way to fix this weakness before it causes problems. They introduce a technique they call LENS, which stands for Lateral Extraction of Neutrino Spectra. Instead of simply using the off-axis data to predict the far detector's view, LENS uses the data to first refine the model of the beam itself. The researchers realized that because the beam is made of different types of particles—primarily pions and kaons that decay into neutrinos—each type responds differently to the angle of observation. By analyzing the data collected at various angles, the LENS method can separate the contributions of these different parent particles. It is like listening to a choir where each singer stands in a slightly different spot; by moving around the room, you can figure out exactly how loud each individual voice is, even if you cannot see them.

The team simulated the DUNE experiment to test how well this approach would work. They created a virtual scenario where the near detector collected data at seven different positions, ranging from directly in the center of the beam to 36 meters to the side. They then used the LENS method to fit the data, adjusting the model to see which combination of pion and kaon contributions best matched the observations. The results were striking. The method was able to determine the strength of the neutrino beam coming from pions with an accuracy of better than two percent, and the beam from kaons with an accuracy of about two to four percent. This is a significant improvement over previous estimates, which suggested uncertainties of around ten percent. The study also showed that this level of precision could be achieved regardless of whether the experiment ran with equal time at all positions or spent half its time in the center, offering flexibility in how the experiment is conducted.

The true power of this discovery lies in how it improves the final measurements. When the researchers applied their refined beam model to predict what the far detector would see, the range of possible outcomes shrank dramatically. In the past, if the initial model of the beam was slightly off, the prediction for the far detector could be biased, leading to incorrect conclusions about neutrino oscillations. With the LENS technique, the model is corrected using real data from the near detector, ensuring that the prediction is much closer to reality. The simulations showed that this reduces the uncertainty in the final results, making the experiment's conclusions about neutrino properties more reliable. Without this correction, the experiment might overestimate or underestimate its sensitivity to key questions, such as the nature of matter-antimatter asymmetry, by a significant margin.

This work highlights a crucial shift in how large-scale physics experiments are designed. In the past, the focus was often on building bigger detectors to gather more statistics. Now, as experiments like DUNE and Hyper-Kamiokande enter an era where systematic errors dominate, the quality of the near detector and the methods used to analyze its data have become just as important as the size of the far detector. The study suggests that highly capable near detectors are not just for checking the beam; they are essential tools for calibrating the entire experiment. By using the near detector to learn about the beam's composition in real-time, scientists can strip away the layers of uncertainty that have long obscured the subtle signals of neutrino physics. The LENS method provides a concrete path forward, turning the near detector into a powerful lens that brings the distant, oscillating neutrinos into sharp focus.

Technical Summary: A LENS on DUNE-PRISM: Characterizing a Neutrino Beam with Off-Axis Measurements

Problem Statement
Upcoming precision long-baseline neutrino oscillation experiments, specifically DUNE and Hyper-Kamiokande, are transitioning from statistics-limited to systematics-limited regimes. A primary source of systematic uncertainty is the imperfect knowledge of neutrino flux predictions and neutrino-nucleus cross sections. While the PRISM (Precision Reaction Independent Spectrum Measurement) technique offers a data-driven method to predict the oscillated far-detector flux by linearly combining near-detector spectra taken at various off-axis angles, this method remains vulnerable to mismodeling of the relative normalizations of different flux components (e.g., neutrinos from pion vs. kaon decays). If the theoretical flux model used to derive the PRISM combination coefficients is biased, the resulting far-detector prediction becomes biased, potentially distorting oscillation measurements.

Methodology
The authors propose and analyze a two-step approach termed LENS (Lateral Extraction of Neutrino Spectra), which complements the standard PRISM prediction:

Flux Model Construction: The neutrino flux is modeled as a sum of five distinct components based on the parent meson species: $K_L$ , $K^+$ , $K^-$ , $\pi^+$ , and $\pi^-$ . The model includes normalization parameters ( $r_p$ ) for each component and allows for spectral tilts.
LENS Fit: Instead of assuming a fixed flux model, the authors perform a frequentist maximum-likelihood fit to simulated off-axis near-detector data (Asimov dataset) collected at seven different angles (from on-axis to 3.59°). This fit simultaneously constrains the flux normalization parameters ( $r_p$ ) and nuisance parameters describing neutrino cross-section uncertainties (quasi-elastic, MEC, resonance, and deep-inelastic scattering normalizations and spectral tilts).
PRISM Integration: The constrained flux model from the LENS fit is then used to calculate the linear combination coefficients ( $c_j$ ) required for the PRISM prediction of the far-detector flux.
Impact Assessment: The authors simulate the DUNE experiment using GLoBES to compare oscillation sensitivity (specifically CP violation discovery potential and parameter contours) under three scenarios:
- Nominal: Using the standard flux model without LENS constraints.
- 5% Variations: Assuming a future improved flux model with 5% uncertainty on components (representing external hadroproduction data).
- LENS Variations: Using the tighter constraints on flux components derived from the LENS fit itself.

Key Contributions

Definition of LENS: The paper formalizes the "Lateral Extraction of Neutrino Spectra" concept, demonstrating that off-axis near-detector measurements can be used to directly constrain the flux model parameters (specifically the relative contributions of different meson species) before applying the PRISM prediction.
Quantification of Flux Constraints: The study quantifies the precision with which DUNE-PRISM can reconstruct individual flux components. It shows that the LENS fit can constrain the normalizations of dominant flux components (like $\pi^+$ and $\pi^-$ ) to better than 2% accuracy, significantly improving upon the typical ~10% prior uncertainties from hadroproduction experiments.
Demonstration of Bias Reduction: The authors demonstrate that without LENS constraints, biases in the assumed flux model (e.g., a 5% shift in component normalizations) can lead to significant errors in the PRISM prediction, potentially shifting oscillation sensitivity by up to $1\sigma$ .

Results

Flux Component Constraints: In a neutrino-dominated beam, the LENS fit constrains the $\pi^+$ flux normalization to ~~1.8% and the $\pi^-$ to ~4.1%. In an anti-neutrino-dominated beam, constraints are similarly tight for $\pi^-$ (~~1.7%) and $\pi^+$ (~~1.8%). Kaon components are constrained to roughly 2–4%, while $K_L$ constraints are weaker (~~10–12%) due to their small contribution to the total flux.
Reduction of Prediction Spread: When applying the PRISM prediction, the spread of possible far-detector spectra is substantially reduced when the coefficients are derived using the LENS-constrained model compared to a model with 5% component uncertainties.
Oscillation Sensitivity:
- CP Violation: The "McDonald's plot" (significance of CP violation discovery vs. true $\delta_{CP}$ ) shows that using the LENS-constrained model prevents the overestimation or underestimation of sensitivity that occurs with biased flux models. The LENS curve closely tracks the "no systematics" ideal curve, whereas the 5% variation curve deviates significantly.
- Parameter Contours: The "superhero" ( $\theta_{13}$ vs. $\delta_{CP}$ ) and "peanut" ( $\theta_{23}$ vs. $\Delta m^2_{31}$ ) plots reveal that LENS constraints significantly reduce the area of the confidence contours, making the results more robust and reliable. The spread in possible outcomes is minimized, bringing the results closer to the statistical limit.

Significance and Claims
The paper claims that while PRISM is a powerful tool for disentangling flux and cross-section uncertainties, its efficacy is limited by the accuracy of the underlying flux model. The LENS technique provides a critical remedy by using the near detector's off-axis capabilities to refine this model directly from data.

The authors conclude that:

Near Detectors are Crucial: Highly capable, movable near detectors are essential for the success of DUNE and Hyper-Kamiokande, not just for cross-section measurements but for characterizing the beam itself.
Systematics Reduction: In the systematics-dominated regime, even modest improvements in flux modeling via LENS lead to substantially improved oscillation results, reducing biases and tightening confidence intervals.
Complementarity: LENS complements external hadroproduction measurements (like NA61/SHINE) and future instrumented decay tunnel concepts (like nuSCOPE), offering a data-driven path to reduce flux uncertainties to the few-percent level required for next-generation precision physics.

The authors remain modest regarding their specific numerical estimates, noting that their flux model is simplified and that a full experimental analysis would require more complex systematic treatments and regularization techniques (e.g., Tikhonov regularization) which were omitted here to isolate the LENS effect. However, the qualitative conclusion—that off-axis data significantly improves flux modeling and thus oscillation sensitivity—is presented as robust.

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