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Tension between MiniBooNE and MicroBooNE within a 3+1 Sterile Neutrino Framework using Simulation-Based Inference

Using a novel simulation-based inference framework to overcome computational and statistical challenges, this study performs a joint analysis of MiniBooNE and MicroBooNE data within a 3+1 sterile neutrino model, revealing a significant tension ( $\geq 2.5\sigma$ ) between the two experiments that reduces the overall preference for sterile neutrinos to $2.7\sigma$ .

Original authors: Julia P. Woodward (Massachusetts Institute of Technology), Austin Schneider (Texas A&M University), Joshua Villarreal (Massachusetts Institute of Technology), John Hardin (Massachusetts Institute of T

Published 2026-09-24

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Original authors: Julia P. Woodward (Massachusetts Institute of Technology), Austin Schneider (Texas A&M University), Joshua Villarreal (Massachusetts Institute of Technology), John Hardin (Massachusetts Institute of Technology), Janet Conrad (Massachusetts Institute of Technology)

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

For decades, physicists have been trying to complete the family portrait of the universe's most elusive residents: neutrinos. These ghostly particles zip through everything, from the Earth to your body, without leaving a trace. The standard model of physics, our best map of how the universe works, predicts that there are three types of these particles, and they can change their identity as they travel, a trick known as oscillation. However, for twenty-five years, a series of experiments have hinted at a fourth, invisible type of neutrino, one that does not interact with the forces that govern the other three. If this "sterile" neutrino exists, it would rewrite the laws of physics, suggesting a hidden layer to reality that we have yet to understand. The question is no longer just whether this fourth particle exists, but whether the conflicting clues left by different experiments can be reconciled into a single, coherent story.

Two major experiments, MiniBooNE and MicroBooNE, have been at the center of this mystery, operating along the same beam of particles at Fermi National Accelerator Laboratory in Illinois. MiniBooNE, which ran for many years, detected a puzzling surplus of electron-like events at low energies, a signal that looked exactly like what a sterile neutrino would produce. This finding was exciting, but it created a problem because other experiments searching for the disappearance of neutrinos suggested a different picture. To solve this, the MicroBooNE experiment was built right next door, using a more advanced detector capable of seeing the details of these interactions with much greater clarity. When MicroBooNE looked at the same beam, it found no evidence for the sterile neutrino, effectively casting doubt on MiniBooNE's earlier discovery. The scientific community was left with a dilemma: two experiments on the same beam, looking at the same phenomenon, telling two different stories.

A team of researchers, led by Julia Woodward and her colleagues, set out to resolve this conflict by treating both experiments with the same rigorous standards. In the past, the two groups had analyzed their data using different mathematical tools and made different assumptions about how to correct for background noise, making a direct comparison difficult. The new study strips away these differences, applying a consistent method to both datasets to see what happens when they are forced to speak the same language. They focused on a specific model that adds just one sterile neutrino to the three known types, testing whether this simple addition can explain the data from both detectors simultaneously.

The researchers used a powerful new technique called simulation-based inference, which relies on machine learning to handle the complex calculations that traditional math struggles with. Instead of relying on standard formulas that assume the data behaves in a predictable, smooth way, they ran millions of simulated experiments to understand exactly how the data should look if the sterile neutrino model were true. This allowed them to fit the MiniBooNE and MicroBooNE data together without forcing the results to fit a preconceived mathematical shape. They also made a crucial decision to remove a specific correction factor that MiniBooNE had previously used to match its predictions to the data, ensuring that the comparison was fair and based on the raw observations rather than adjusted numbers.

The results of this joint analysis paint a picture of significant disagreement. When the data from both experiments are combined, the strong signal that MiniBooNE saw on its own is greatly weakened, dropping to a level of statistical significance that is no longer considered a definitive discovery. More importantly, the study found that the two experiments are in direct tension with each other. The researchers calculated that there is a statistical conflict of at least 2.5 standard deviations between the two datasets. In the language of physics, this means that the preferred settings for the sterile neutrino model in MiniBooNE are incompatible with the settings preferred by MicroBooNE. It is as if two witnesses describing the same event are telling stories that cannot both be true, even when you account for the possibility that one might be slightly mistaken.

This tension suggests that the simple idea of adding just one sterile neutrino to the universe is likely insufficient to explain the anomalies seen in these experiments. While the MiniBooNE excess remains a real feature of the data, the MicroBooNE detector, with its superior ability to distinguish between different types of particles, does not see the same signal. The study concludes that the two experiments cannot be easily unified under the current model, indicating that the source of the discrepancy is not just a matter of different analysis methods, but a fundamental mismatch in what the detectors are observing. The mystery of the low-energy excess remains, but the path to solving it likely requires looking beyond the simplest version of the sterile neutrino theory, or perhaps re-examining the very nature of the neutrino interactions themselves.

Technical Summary: Tension between MiniBooNE and MicroBooNE within a 3+1 Sterile Neutrino Framework using Simulation-Based Inference

Problem Statement
The MiniBooNE experiment observed a significant low-energy excess (LEE) of electron-like events, consistent with a 3+1 sterile neutrino model, while the MicroBooNE experiment, operating on the same Booster Neutrino Beam (BNB) line, reported no evidence for such a signal. This discrepancy creates a tension between appearance and disappearance searches in short-baseline neutrino anomalies. However, a rigorous joint analysis has been hindered by methodological inconsistencies between the two collaborations. Specifically, MiniBooNE and MicroBooNE employ different statistical frameworks (Wilks' theorem vs. frequentist CLs) and different treatments of data-driven corrections (specifically the $f_\pi$ factor used to rescale charged pion decay events). Furthermore, existing methods for quantifying the "Parameter Goodness-of-Fit" (PG) tension rely on asymptotic assumptions (Wilks' theorem) that are known to be inaccurate for neutrino oscillation measurements involving sinusoidal signals, or require computationally prohibitive repeated likelihood optimizations (Feldman-Cousins).

Methodology
To address these challenges, the authors present a unified analysis framework that treats both MiniBooNE and MicroBooNE data consistently.

Unified Data Treatment: The analysis removes the data-driven $f_\pi$ correction from the MiniBooNE prediction to ensure consistency with MicroBooNE, which did not apply such a factor. This allows for a direct comparison of the underlying physics without post-hoc scaling factors that may differ between experiments. The analysis utilizes MicroBooNE data from both the BNB and Neutrinos at the Main Injector (NuMI) beamlines to break degeneracies between $\nu_e$ appearance and disappearance.
Simulation-Based Inference (SBI): To overcome the limitations of Wilks' theorem and the computational cost of traditional frequentist methods, the authors employ a Simulation-Based Inference framework.
- Likelihood Ratio Estimation: A neural network classifier (Direct Amortized Neural Likelihood Estimator, or DNRE) is trained on simulated pseudo-experiments to approximate the likelihood ratio between physics parameters.
- Posterior Estimation: A Sequential Neural Posterior Estimator (SNPE-C) is used to determine the best-fit parameters.
- Frequentist Calibration: Confidence levels are constructed using a trials-based approach (analogous to Feldman-Cousins) but accelerated by SBI, ensuring correct coverage properties without relying on asymptotic assumptions.
SBI-based PG Tension: The authors introduce a novel SBI-based method to evaluate the PG tension. Since absolute $\chi^2$ values are inaccessible in the network framework, they define a tension statistic ( $\hat{T}_{PG}$ ) based on the difference in log-likelihood ratios between the global fit and the sum of individual experiment fits. This is calibrated using 48,000 null realizations to generate empirical distributions.

Key Results

Joint Fit Significance: When fitting both MiniBooNE (without $f_\pi$ ) and MicroBooNE (BNB + NuMI) data to a 3+1 sterile neutrino model using the SBI framework, the preference for the 3+1 model is reduced to 2.7 $\sigma$ . This is a substantial reduction compared to the >5 $\sigma$ preference often seen in global fits that do not account for the specific MicroBooNE constraints or the consistent treatment of systematics.
Parameter Tension: The analysis reveals a $\ge$ 2.5 $\sigma$ PG tension between the MiniBooNE and MicroBooNE datasets within the 3+1 model. This indicates that the preferred regions of parameter space for the two experiments are not fully compatible.
Impact of $f_\pi$ : The removal of the $f_\pi$ correction from the MiniBooNE fit significantly increases the signal significance of the MiniBooNE-only fit (from 4.8 $\sigma$ to 7.1 $\sigma$ in Wilks-based calculations) and increases the tension between the experiments. However, even with consistent treatment of $f_\pi$ , a statistically significant tension ( $\ge$ 2 $\sigma$ ) persists, suggesting the disagreement is not solely due to the $f_\pi$ factor but likely stems from deeper issues in the modeling of $\nu_\mu$ excesses or nuclear effects.
Methodological Validation: The SBI-based results show qualitative agreement with Wilks-based calculations but differ quantitatively, particularly in the high-significance regime where Wilks' theorem is known to under-cover. The SBI approach provides a more robust frequentist treatment for these oscillatory signals.

Significance and Claims
The paper claims to provide the first consistent joint fit of MiniBooNE and MicroBooNE data to a 3+1 sterile neutrino model using both BNB and NuMI datasets without the MiniBooNE $f_\pi$ correction. The primary significance lies in demonstrating that the 3+1 model struggles to simultaneously describe both datasets, exhibiting a moderate tension ( $\ge$ 2.5 $\sigma$ ) that challenges the viability of a minimal sterile neutrino explanation for the observed anomalies.

Methodologically, the authors claim to have established a complete framework for conducting entirely SBI-based global fits. This includes a computationally feasible method for evaluating PG tension that avoids the inaccuracies of asymptotic assumptions and the intractability of traditional trial-based methods. The authors suggest this framework is essential for evaluating more complex sterile neutrino scenarios (e.g., 3+2 or 3+3) and for assessing tensions in other particle physics contexts where multiple experiments disagree with a common theoretical model. The work concludes that while the 3+1 preference is reduced, the persistent tension highlights the need for further understanding of the underlying systematic discrepancies, particularly regarding $\nu_\mu$ event rates and nuclear effects.

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