⚛️ nuclear theory

Spectral function approach in NuWro: modeling of multinucleon final states in quasielastic scattering

This paper presents an updated implementation of the spectral function approach in the NuWro Monte Carlo generator that consistently models multinucleon final states in quasielastic scattering, demonstrating significantly improved agreement with MicroBooNE neutrino cross-section data compared to previous models.

Original authors: Artur M. Ankowski, Rwik Dharmapal Banerjee, Jan T. Sobczyk, José L. Bonilla, Krzysztof M. Graczyk, Beata E. Kowal, Hemant Prasad

Published 2026-10-14

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CC BY 4.0

Original authors: Artur M. Ankowski, Rwik Dharmapal Banerjee, Jan T. Sobczyk, José L. Bonilla, Krzysztof M. Graczyk, Beata E. Kowal, Hemant Prasad

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

To understand the story of the universe, physicists often look at the smallest particles, specifically a ghostly particle called the neutrino. These particles are produced in vast numbers by the sun and by powerful machines on Earth, and they pass through ordinary matter almost without a trace. Because they interact so rarely, scientists must build enormous detectors to catch even a few of them. One of the most important goals in modern physics is to measure how these neutrinos change, or "oscillate," as they travel. This phenomenon holds the key to understanding why the universe is made of matter rather than antimatter. However, to measure this change accurately, scientists must first understand exactly how a neutrino behaves when it finally hits a detector. When a neutrino strikes an atom inside the detector, it does not hit a single, isolated particle; it hits a tightly packed nucleus, a dense cluster of protons and neutrons that are constantly jostling and interacting with one another. Predicting the outcome of this collision is incredibly difficult because the rules of physics change when particles are crowded together in this way.

A team of researchers has developed a new way to simulate these complex collisions, improving the accuracy of the computer programs used to interpret data from major experiments. The scientists focused on a specific type of interaction called quasielastic scattering, where a neutrino hits a proton or neutron inside an atom and knocks it out. In the past, computer models often assumed that the struck particle was alone and that the other particles in the nucleus simply watched from the sidelines. This paper shows that this assumption is too simple. The researchers updated a widely used computer simulation tool called NuWro to account for the fact that when a neutrino hits one particle, it often drags a neighbor along with it. They also refined how the simulation handles the chaos that happens after the collision, as the knocked-out particle fights its way through the remaining crowd of nuclear matter. By including these "multinucleon" effects and the messy aftermath of the crash, the new model matches real-world data much more closely than previous versions did.

The researchers tested their updated model against data from the MicroBooNE experiment, which uses a massive tank of liquid argon to catch neutrinos. They looked at two specific scenarios: cases where the collision produced exactly one proton and no pions, and cases where it produced exactly two protons and no pions. In the past, the computer models struggled to reproduce the shape and size of the data collected by MicroBooNE, often missing the mark by a significant margin. The new approach, which treats the nucleus as a dynamic system where particles are linked and interact, fixed these problems. When the team included the effects of particles being knocked out together and the subsequent interactions within the nucleus, their predictions aligned with the experimental data with a high degree of precision. The statistical measure of how well the model fit the data improved dramatically, dropping from values that indicated a poor match to values that indicated a very good agreement.

A crucial part of this improvement came from a better understanding of how the nucleus is built. For the argon target, the team incorporated a detailed map of how protons and neutrons are arranged, distinguishing between those that sit quietly in their own orbits and those that are tightly bound in pairs, moving in a coordinated dance of short-range attraction. When a neutrino hits one of these paired particles, the model now correctly predicts that the partner is also ejected. This "correlated" behavior explains why the detector sees more two-proton events than older models could account for. Furthermore, the team improved how the simulation handles the "final state interactions," which are the collisions that occur after the initial hit, as the escaping particles bounce off other nucleons in the nucleus. They adjusted the model to reflect that these escaping particles lose energy and change direction as they push through the nuclear medium, a process that significantly alters the final signal seen by the detector.

The study also revealed that the current understanding of how particles move through the nucleus might still be slightly incomplete. While the new model fits the data much better, the researchers found that their simulation still slightly underestimates how much energy is absorbed by the nucleus during these collisions. This suggests that the "intranuclear cascade," the process by which particles bounce around inside the nucleus, might be too gentle in the current computer code. The team noted that their optical potentials, which describe the forces acting on the escaping particles, were derived from data involving protons bouncing off nuclei at different speeds. They suspect these forces might not be perfectly accurate when applied to the specific, high-energy conditions of neutrino collisions. This uncertainty highlights a gap in knowledge that future experiments on oxygen and argon will need to fill.

Ultimately, this work provides a more reliable foundation for the next generation of neutrino experiments. By showing that accounting for the complex, crowded nature of the atomic nucleus is essential for accurate predictions, the researchers have removed a major source of error from the field. Their updated simulation allows scientists to trust the data from experiments like MicroBooNE and future projects with greater confidence. The findings confirm that to truly understand the neutrino, one must look beyond the single particle and embrace the complexity of the entire nuclear family. As the field moves toward even more precise measurements, these improved models will be the key to unlocking the secrets of the universe's most elusive particles.

Technical Summary: Spectral Function Approach in NuWro: Modeling of Multinucleon Final States in Quasielastic Scattering

Problem Statement
Next-generation accelerator-based neutrino-oscillation experiments operating in the few-GeV energy region face stringent precision goals that are currently limited by uncertainties in modeling neutrino interactions with nuclear targets, particularly oxygen and argon. A primary source of these uncertainties is the accurate description of quasielastic (QE) scattering, specifically the treatment of multinucleon final states and final-state interactions (FSI). Previous implementations in Monte Carlo (MC) generators, including earlier versions of NuWro, often relied on the Plane-Wave Impulse Approximation (PWIA) or distorted-wave approaches that underestimated experimental data for charged-current (CC) cross sections involving one or two protons without pions (CC1p0π and CC2p0π). Literature suggests that two-nucleon knockout contributions and interference between one- and two-body currents are critical missing components.

Methodology
The authors present an updated implementation of the Spectral Function (SF) approach within the NuWro Monte Carlo generator (version 25.11). This update aims to consistently treat inclusive and exclusive QE processes for targets ranging from carbon to iron, with a specific focus on argon for the Fermilab short-baseline program (SBND, MicroBooNE, ICARUS).

The methodology involves two primary technical advancements:

Final-State Interactions (FSI) via Convolution Scheme:
To account for FSI effects on QE scattering, the authors implement a convolution scheme that integrates PWIA predictions with a folding function. This function models the broadening of the cross section and the shift in the energy spectrum caused by interactions between the struck nucleon and the spectator system.
- Broadening: Modeled by a finite-width function $F_q(\omega)$ , applied to events where the struck nucleon initiates an intranuclear cascade ("nontransparent" events).
- Energy Shift: Modeled by incorporating the real part of the optical potential, $U_V(t_{kin})$ , into the folding function argument. These potentials are derived from Dirac phenomenological fits to proton elastic scattering data.
- Nuclear Transparency ( $T_A$ ): The fraction of transparent events is determined using $T_A$ values derived from theoretical calculations and experimental $(e, e'p)$ data, extended to oxygen and argon based on mass-number scaling.
Correlated Spectral Functions for Argon:
For the argon target, the implementation separates the SF into mean-field (MF) and correlated parts.
- Mean-Field: Describes individual nucleons in shell-model states (~80% of strength).
- Correlated: Models nucleons involved in short-range correlations (SRC), primarily quasi-deuteron pairs ($pn$), contributing ~20% of the strength. The correlated part is modeled using a specific formalism (Ref. [47]) that accounts for center-of-mass and relative momentum distributions of the nucleon pairs. This allows for the simulation of correlated nucleon kinematics, where the struck nucleon is associated with a correlated partner at the primary vertex.

Key Contributions

Implementation: The integration of FSI effects and correlated spectral functions into NuWro for both electron and neutrino scattering modes.
Argon Modeling: A detailed model for argon that includes short-range correlations, addressing the specific needs of the MicroBooNE experiment.
Validation Framework: A rigorous validation strategy comparing NuWro predictions against inclusive electron-scattering data on carbon and exclusive neutrino cross-section data from MicroBooNE.

Results
The authors validated the model against inclusive electron-scattering data on carbon. The inclusion of FSI (optical potential shifts and broadening) significantly improved the reproduction of the QE peak position and shape, particularly at lower kinetic energies. However, discrepancies remained at higher kinetic energies, suggesting that optical potentials derived from elastic scattering may not fully capture inelastic or two-body interaction mechanisms in the QE region.

When applied to MicroBooNE data:

CC2p0π (Two-proton, zero-pion): The model with FSI and correlated protons reproduced the differential cross sections ( $d\sigma/d\cos\theta_{pp}$ , $d\sigma/d\cos\theta_{\mu2p}$ , $d\sigma/d\delta p_T$ ) with $\chi^2$ per degree of freedom ranging from 0.82 to 2.54. In contrast, the model without these features yielded $\chi^2$ values between 2.33 and 6.21, failing to reproduce both normalization and shape.
CC1p0π (One-proton, zero-pion): The full model improved the description of the transverse kinematic imbalance variables ( $\delta\alpha_T$ , $\delta p_T$ ). While the shape agreement was "much better" than the model without FSI, a deficit in normalization remained in the high-momentum transfer region, suggesting that absorptive processes in the intranuclear cascade may still be underestimated. The experimental $d\sigma/d\delta\alpha_T$ cross section was reproduced "rather well," quantified by a $\chi^2$ of 1.58 per degree of freedom (compared to 7.32 without FSI), though this indicates a less perfect fit than the CC2p0π results.

Sensitivity analyses indicated that the results are moderately sensitive to uncertainties in nuclear transparency ( $\pm 3\%$ ) and the real part of the optical potential. Capping the optical potential to account for its shallowness at high kinetic energies improved the fit for the $\delta\alpha_T$ distribution.

Significance
The paper claims that accounting for FSI and correlated nucleons is essential for bringing NuWro predictions into good agreement with experimental data for multinucleon final states. The results demonstrate that non-QE channels (such as meson-exchange currents and two-nucleon knockout) make sizable contributions to the observed cross sections.

The authors conclude that while the current implementation represents a significant step forward, the community urgently requires new measurements of inclusive electron-scattering cross sections, particularly on oxygen and argon, covering the kinematics relevant to neutrino-oscillation experiments. Such data are necessary to refine optical potentials and nuclear transparency models, which are prerequisites for realizing the full physics potential of next-generation neutrino-oscillation programs. The paper modestly notes that current optical potentials derived from elastic data may not be accurate in kinematic regions where QE scattering overlaps significantly with resonance production or other interaction mechanisms.

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