Benchmarking neutrino-nucleus quasielastic scattering model predictions against a missing energy profile obtained using a monoenergetic neutrino beam

This paper benchmarks three exclusive nuclear ground-state shell models implemented in the NEUT neutrino event generator against recent JSNS$^2$ measurements of missing energy from a monoenergetic neutrino beam, finding that spectral function models outperform relativistic mean field models and that accounting for missing energy thresholds allows all tested nuclear models to be statistically accepted.

The Gist

The Big Picture: Why Do We Need This?

Imagine you are trying to figure out what's inside a sealed, opaque box by throwing a ball at it and watching how the ball bounces back. This is essentially what physicists do when they study neutrinos (tiny, ghost-like particles) hitting an atomic nucleus (the core of an atom).

For decades, scientists have been using computer programs (called "event generators") to predict how these collisions happen. These programs are like recipe books for physics simulations. However, the recipes for how the "ingredients" inside the nucleus (protons and neutrons) behave have been a bit fuzzy.

The problem is that most neutrino beams are like a rainstorm: they contain neutrinos of all different energies hitting the target at once. This makes it hard to tell if a weird result in the data is because the neutrino hit something strange, or just because the "weather" (the energy mix) was messy.

The New Tool: A "Laser Pointer" for Neutrinos

This paper focuses on a special experiment called JSNS2. Instead of a rainstorm, they used a monoenergetic beam. Think of this as a laser pointer made of neutrinos. Every single neutrino in the beam has the exact same energy (235.5 MeV).

Because the "laser" is so precise, the scientists can measure something called "Missing Energy."

• The Analogy: Imagine you throw a billiard ball at a cluster of marbles. You know exactly how much energy you threw. After the crash, you measure the energy of all the pieces that fly out. If the total energy of the flying pieces is less than what you threw in, that "missing" energy went into shaking the remaining cluster or breaking bonds inside it.
• In this experiment, the "missing energy" tells us exactly how the neutrons were arranged inside the Carbon-12 nucleus before the hit.

The Contenders: Three Different "Recipes"

The authors took three different "recipes" (theoretical models) used in the NEUT computer program and tested them against the JSNS2 laser data.

1. The Spectral Function (SF) Models: Think of these as detailed maps. They are based on real data from electron scattering experiments. They try to draw a precise picture of where every neutron is and how much energy it takes to knock one out. There were two versions:
   • SF: The original map.
   • SF*: A high-definition upgrade that separates specific energy levels that were previously blurred together.
2. The ED-RMF Model: Think of this as a theoretical blueprint. Instead of relying on a map of the past, it uses complex math (Relativistic Mean Field theory) to calculate how the nucleus should behave based on fundamental laws of physics.

The Simulation: Adding the "Chaos"

When a neutrino hits a nucleus, it doesn't just knock one particle out and leave. It's like a pinball machine. The knocked-out particle hits other particles, which hit others, and the whole nucleus might glow (emit gamma rays) as it settles down.

The paper tested the models in three stages:

1. The Clean Hit: Just the initial collision (no chaos).
2. The Pinball Effect: Adding the Intranuclear Cascade (particles bouncing around inside).
3. The Aftermath: Adding NucDeEx (the nucleus cooling down and emitting light/particles).

The Results: Who Won the Race?

Here is how the models fared against the "laser" data:

• The Clean Hit (No Chaos): All three models struggled. They predicted the nucleus would be too "stiff" or too "soft" in the wrong places. The theoretical blueprint (ED-RMF) and the high-def map (SF*) both predicted a peak in energy that was too high compared to reality.
• Adding the Pinball (Cascade): This was the game-changer. When the scientists let the particles bounce around inside the nucleus (simulating the real chaos), the models got much better.
  • The SF model (the original map) became the champion. It matched the data almost perfectly.
  • The SF* and ED-RMF models improved but still had some issues. They tended to overestimate how much energy was needed to knock a particle out, creating a "hump" in the data that didn't exist in the real experiment.

The "Threshold" Twist:
There is a physical rule: You need a minimum amount of energy to knock a single neutron out of a carbon atom (about 18.7 MeV).

• The ED-RMF model accidentally predicted that you could knock a neutron out with less energy than physically possible (a mathematical glitch in how they smoothed the data).
• When the scientists applied a "cutoff" to ignore these impossible low-energy predictions, all three models passed the test.

The Takeaway

1. Precision Matters: Using a "laser" beam of neutrinos allowed scientists to see flaws in the computer models that a "rainstorm" beam would have hidden.
2. Chaos is Key: You cannot accurately simulate neutrino collisions without accounting for the "pinball" effect of particles bouncing inside the nucleus.
3. The Winner: The Spectral Function (SF) model, which relies on real-world electron scattering data, currently does the best job of describing how neutrons sit inside a Carbon nucleus.
4. The Lesson: Even our best theoretical blueprints (ED-RMF) need to be tweaked to match the messy reality of how particles actually bounce around.

In short: The paper is like a car review. The scientists took three different car models (theoretical predictions), drove them on a perfectly smooth test track (the monoenergetic beam), and found that while the theoretical blueprints looked great on paper, the car built on real-world data (SF) drove the smoothest. They also learned that you have to account for the "bumps in the road" (the nuclear cascade) to get an accurate picture.

Technical Summary

1. Problem Statement

Precise modeling of neutrino-nucleus interactions is critical for current and future neutrino oscillation experiments (e.g., T2K, DUNE, Hyper-K). Systematic uncertainties arising from nuclear effects significantly impact the reconstruction of neutrino energy and the interpretation of signals.

• The Challenge: Most neutrino beams have a broadband energy spectrum, which smears out final-state observables and makes it difficult to disentangle nuclear ground-state modeling from other nuclear effects (like Final State Interactions, or FSI).
• The Opportunity: Neutrinos produced by Kaon Decay At Rest (KDAR) offer a monoenergetic source ($E_\nu = 235.5$ MeV). This allows for a precise measurement of the missing energy ($E_m$) profile, which directly probes the neutron spectral function (the distribution of nucleon removal energies and momenta) in the target nucleus ($^{12}\text{C}$).
• The Gap: While neutrino event generators (like NEUT) have implemented exclusive nuclear models (Spectral Function and Relativistic Mean Field), they have primarily been validated against inclusive electron scattering or broadband neutrino data. There is a lack of rigorous benchmarking against exclusive, monoenergetic neutrino data that can resolve fine details of the nuclear ground state and the high-energy tail.

2. Methodology

The authors benchmarked three exclusive nuclear ground-state models implemented in the NEUT neutrino event generator (v6.0.3) against the first missing energy spectrum measurement from the JSNS2 collaboration using a KDAR source on a carbon target.

Models Tested:

1. Benhar Spectral Function (SF): Derived from $(e, e'p)$ electron scattering data. It provides a 2D probability $P(p, \tilde{E})$ for removing a proton with momentum $p$ and removal energy $\tilde{E}$. A neutron correction is applied to account for the Coulomb potential difference.
2. Benhar Spectral Function (SF):* A newer version with higher resolution that distinguishes between the ground state and the first two excited states of $^{11}\text{B}^*$ (and by extension $^{11}\text{C}^*$ for neutrons), which were previously smeared out.
3. Energy-Dependent Relativistic Mean Field (ED-RMF): An unfactorized model where initial and final states are treated in a consistent theoretical framework using relativistic optical potentials. It uses Gaussian shells to model the missing energy profile.

Simulation Components:

• FSI (Final State Interactions): The NEUT intranuclear cascade (based on the Bertini model) was used to simulate inelastic rescattering.
• NucDeEx: A dedicated nuclear de-excitation generator was used to simulate gamma-ray and light particle emissions from excited residual nuclei.
• Threshold Handling: The authors performed comparisons both with and without applying a physical cutoff at the Single Nucleon Knockout (1NKO) threshold ($S_n = 18.72$ MeV for $^{12}\text{C}$). This is crucial because some models (SF and ED-RMF) theoretically predict unphysical events below this threshold due to their Gaussian parameterizations.

Analysis Strategy:

• Generated samples were processed using the NUISANCE framework.
• A $\chi^2$ analysis was performed comparing the simulated missing energy distributions to the JSNS2 data.
• Covariance matrices (statistical, proton Birks' constant, and generator systematics) were utilized.
• A $\chi^2_{N-1}$ analysis was conducted to identify which specific energy bins contributed most to the disagreement.

3. Key Contributions

• First Exclusive Benchmark: This is the first study to benchmark exclusive nuclear models in NEUT against a monoenergetic neutrino missing energy spectrum, providing a unique probe of the neutron spectral function in $^{12}\text{C}$.
• Disentangling Effects: The study successfully isolates the impact of the nuclear ground-state model from inelastic FSI and nuclear de-excitation by sequentially enabling these components.
• Threshold Sensitivity: The paper highlights that the 1NKO threshold is a critical discriminator. Without it, models with unphysical low-energy tails are penalized; with it, the sensitivity to the ground-state peak structure is reduced, changing the statistical acceptance of the models.
• Parameter Sensitivity: The authors investigated the sensitivity of the ED-RMF model to shell occupancy and width parameters, as well as the impact of varying the FSI strength in the NEUT cascade.

4. Results

Without FSI and De-excitation:

• All three models (SF, SF*, ED-RMF) were rejected ($p < 0.05$).
• The SF model reproduced the height of the $1p_{3/2}$ ground-state peak reasonably well.
• The SF* and ED-RMF models overestimated the $1p_{3/2}$ peak.
• All models failed to reproduce the distribution tail (high missing energy), lacking the strength provided by nucleon rescattering.

With NEUT FSI Cascade (Inelastic):

• Improvement: Including the FSI cascade shifted strength from the ground-state peak to the tail, significantly improving the $\chi^2$ for all models.
• SF Model: Became statistically accepted ($p = 0.78$) without the 1NKO threshold.
• SF and ED-RMF:* Remained rejected ($p \approx 0.00$). The ED-RMF model performed worst in the tail region.
• Discrepancy Source: The SF* model overestimated the peak and underestimated the transition region between the $1p_{3/2}$ and $1s_{1/2}$ peaks. The ED-RMF model's Gaussian parameterization introduced non-physical strength below the 1NKO threshold.

With FSI and NucDeEx (De-excitation):

• The de-excitation routine slightly shifted strength back toward the $1p_{3/2}$ peak.
• Without 1NKO threshold: Only the SF model was accepted. SF* and ED-RMF were rejected.
• With 1NKO threshold: All models were accepted ($p > 0.05$). However, the $\chi^2_{N-1}$ analysis revealed that the SF* model's agreement was still driven by the transition region between peaks, while the SF and ED-RMF models were driven by the tail.

Appendix Findings:

• Potentials: Changing the final-state potential in ED-RMF (e.g., to RPWIA) improved results slightly but did not fundamentally change the rejection status without FSI.
• FSI Strength: Increasing the FSI strength by 30% significantly improved the agreement for the SF model (reducing $\chi^2$) and slightly improved ED-RMF, suggesting the default NEUT cascade might underestimate rescattering.

5. Significance and Conclusion

• Model Validation: The Benhar Spectral Function (SF) model, when combined with the NEUT FSI cascade, provides the best agreement with the JSNS2 monoenergetic data. The more theoretically rigorous ED-RMF and the high-resolution SF* models are currently excluded by the data, primarily due to issues in modeling the ground-state peak shape and the transition region.
• Implications for Oscillation Experiments: While broadband neutrino beams often mask these detailed discrepancies, this study proves that exclusive, monoenergetic measurements are essential for validating the nuclear spectral functions used in generators.
• Future Directions: The study suggests that:
  1. The SF* model needs refinement in the transition region between shell peaks.
  2. The ED-RMF model requires a non-Gaussian (single-sided) approach for the ground state to avoid unphysical low-energy tails.
  3. The FSI strength in NEUT may need to be increased to better match the data.
  4. Future work should compare different FSI cascades (e.g., NuWro) to isolate cascade effects from nuclear ground-state modeling.

In summary, this paper demonstrates that while modern event generators are improving, there are still significant, quantifiable discrepancies in how they model the neutron spectral function of carbon, which can only be resolved using high-precision, monoenergetic neutrino data.