A Simulation-Based Inference Evaluation of Tension Between MicroBooNE and MiniBooNE Results in a 3+1 Sterile Neutrino Global Fit

This paper introduces a Simulation-Based Inference framework to quantify the tension between MicroBooNE and MiniBooNE datasets within a 3+1 sterile neutrino global fit, revealing a significant $3.3\sigma$ disagreement that relaxes to $2.2\sigma$ after correcting for MicroBooNE normalization differences, thereby highlighting both model limitations and systematic uncertainties.

The Gist

Imagine you are a detective trying to solve a mystery about the universe, specifically the behavior of tiny, ghost-like particles called neutrinos. For years, scientists have been trying to figure out if there is a "fourth" type of neutrino (a "sterile" one) hiding in the shadows, which would change our understanding of physics.

This paper is like a report from a team of detectives who are using a new, high-tech method to check if the clues they've gathered actually fit together.

The Big Mystery: The "3+1" Theory

Think of the standard model of physics as a puzzle with three pieces that fit perfectly. The "3+1" theory suggests there's a fourth piece (the sterile neutrino) that makes the picture even more complete.

Two famous experiments, MiniBooNE and MicroBooNE, are like two different witnesses at a crime scene. They are both looking at the same stream of particles (the "beamline") to see if this fourth piece exists.

• MiniBooNE says, "I definitely saw the fourth piece!"
• MicroBooNE says, "I'm not so sure, I didn't see it as clearly."

The Old Problem: The "Math vs. Reality" Trap

In the past, scientists tried to combine these two witnesses' stories using standard math (called a "chi-squared fit"). The math said, "Hey, if we add this fourth piece, the whole story looks 5 times more likely to be true than the old story without it!"

But here's the catch: Even though the math loved the new theory, the two witnesses were still glaring at each other. One said "Yes," and the other said "No." It's like a jury deciding a defendant is guilty based on a strong alibi, but two key witnesses are screaming that they saw two different things. The model might be mathematically "better," but it's failing to explain the specific details of the data.

The New Tool: A "Simulation Detective"

This paper introduces a new tool called Simulation-Based Inference (SBI).

Imagine you have a super-smart AI that can run millions of virtual crime scenes in a second. Instead of just doing math on paper, this AI simulates what the universe would look like if the "3+1" theory were true, and then compares those simulations to the real data from MiniBooNE and MicroBooNE.

This is the third time this team has used this AI. The first two times, they used it just to see if the theory fit the data quickly. This time, they used it to measure the "tension" (the disagreement) between the two experiments.

What They Found

When they ran their new AI simulation:

1. MiniBooNE still looked very convinced (3.6 out of 5 stars of confidence).
2. MicroBooNE was a bit more skeptical (1.8 out of 5 stars).
3. The Tension: The AI calculated that the two experiments disagreed with each other by 3.3 stars. This is a huge gap. It means the "3+1" theory is struggling to explain both stories at the same time.

The Twist: A Calibration Glitch

Then, the detectives noticed something. The MicroBooNE experiment had a slight "volume knob" issue—its numbers were a bit too loud or too quiet compared to the computer simulations.

When they turned the volume knob down (corrected for this difference), the tension dropped from 3.3 to 2.2.

• Translation: The disagreement got smaller, but it didn't disappear. They are still arguing, just a little less loudly.

The Bottom Line

The paper concludes that while the idea of a "fourth neutrino" is tempting and makes the overall math look better, the two experiments are still telling conflicting stories.

This conflict could mean two things:

1. The Theory is Wrong: The "3+1" model is too simple to explain the complex reality of neutrinos.
2. The Tools are Flawed: There are hidden errors in how the experiments measure things that affect them differently.

In short: The scientists built a faster, smarter way to check their work. They found that while the "fourth neutrino" idea is popular, the evidence is still messy and contradictory. They need to either find a more complex theory or fix their measuring tools before they can solve the mystery.

Technical Summary

1. Problem Statement

The core problem addressed is the persistent statistical tension between different neutrino oscillation datasets when analyzed under the 3+1 sterile neutrino hypothesis (a model proposing four neutrino mass states: three active and one sterile).

• The Conflict: While the 3+1 model shows a significant overall improvement ($>5\sigma$) over the Standard Model ($3\nu$) in global fits, there is a fundamental incompatibility between datasets sensitive to $\nu_e$ appearance (excess events) and those sensitive to $\nu_e/\nu_\mu$ disappearance (deficit events).
• The Bottleneck: Evaluating more complex models that could resolve this tension is currently computationally prohibitive. Traditional global fits using $\chi^2$ minimization are slow, hindering the exploration of the high-dimensional parameter spaces required for robust model selection.
• Specific Context: The paper focuses on the specific tension between the MiniBooNE experiment (which observed a low-energy excess consistent with $\nu_e$ appearance) and the MicroBooNE experiment (which, using the same beamline, did not observe a corresponding excess in charged-current quasi-elastic interactions).

2. Methodology

The authors employ Simulation-Based Inference (SBI) as a novel framework to address computational costs and rigorously define statistical tension.

• SBI Framework: This is the third paper in a series developing SBI for global fits. Unlike traditional methods that rely on likelihood approximations, SBI uses neural networks to learn the posterior distribution directly from simulations, drastically reducing computational time.
• Tension Definition: The authors formalize a specific definition of "tension" within the SBI framework. This allows for a quantitative assessment of how incompatible two datasets are under a specific model hypothesis.
• Data Sets:
  • MiniBooNE: Charged-current quasi-elastic (CCQE) neutrino data.
  • MicroBooNE: Inclusive neutrino data.
• Analysis Strategy:
  1. Perform a full 3+1 global fit to both datasets simultaneously using the SBI procedure.
  2. Utilize experiment-supplied systematics without initial modification to establish a baseline.
  3. Conduct a secondary analysis correcting for normalization differences between data and Monte Carlo (MC) in the MicroBooNE $\nu_\mu$ samples to test the sensitivity of the tension to systematic uncertainties.

3. Key Contributions

• Formalization of Tension in SBI: The paper provides a rigorous mathematical definition of dataset tension specifically tailored for the Simulation-Based Inference paradigm, moving beyond simple $\chi^2$ differences.
• Computational Efficiency: It demonstrates the viability of SBI for complex, high-dimensional global fits involving multiple experiments, paving the way for evaluating more complex sterile neutrino models that were previously too computationally expensive.
• Systematic Sensitivity Analysis: The work explicitly quantifies how normalization uncertainties in MicroBooNE data impact the global fit results, offering a nuanced view of the disagreement between the two experiments.

4. Key Results

The application of the SBI framework yielded the following statistical findings:

• Individual Preferences (Baseline):
  • MiniBooNE: Favors the 3+1 hypothesis at $3.6\sigma$.
  • MicroBooNE: Favors the 3+1 hypothesis at $1.8\sigma$.
• Baseline Tension: When fitting both datasets simultaneously with uncorrected systematics, the tension between them is $3.3\sigma$. This indicates a significant disagreement where the 3+1 model cannot simultaneously satisfy both datasets.
• Corrected Tension: After applying corrections for normalization differences in the MicroBooNE $\nu_\mu$ samples:
  • The tension relaxes to $2.2\sigma$.
  • While reduced, this level of disagreement remains non-negligible, suggesting the tension is not solely an artifact of normalization errors.

5. Significance and Implications

• Model Limitations: The persistent tension (even after corrections) suggests that the 3+1 sterile neutrino model may be insufficient to describe the combined dataset. The model likely fails to capture the underlying physics or systematic behaviors of the experiments simultaneously.
• Systematic Effects: The results highlight that systematic effects impacting MiniBooNE and MicroBooNE differently play a crucial role in the observed discrepancies.
• Future Directions: The findings motivate the development of more complex models beyond 3+1. The SBI framework established in this paper is critical for the future evaluation of these complex models, as it offers a computationally feasible path to explore the parameter spaces necessary to resolve the MiniBooNE/MicroBooNE anomaly.

In summary, this paper utilizes advanced Simulation-Based Inference to quantify the incompatibility between MiniBooNE and MicroBooNE data within the 3+1 sterile neutrino framework. While the tension is partially mitigated by correcting for normalization systematics, a significant disagreement remains, pointing toward the need for more sophisticated theoretical models and robust computational tools to interpret neutrino oscillation anomalies.