Comparisons of triple-differential cross sections for quasielastic-like $\nu_\mu$-hydrocarbon interactions using $\langle E_\nu\rangle \sim$ 3~GeV versus $\sim$ 6~GeV beams in MINERvA

This MINERvA study compares triple-differential cross sections for quasielastic-like $\nu_\mu$-hydrocarbon interactions in 3 GeV and 6 GeV beams to test neutrino interaction models, revealing discrepancies that indicate an overestimation of final-state interactions for protons and charged pions in current simulations.

The Gist

Imagine you are trying to figure out how fast a car was going just before it crashed into a wall. You can't see the car anymore, but you can measure the speed of the debris flying off the wall and the angle at which it hit. In the world of particle physics, scientists do something similar with neutrinos—tiny, ghost-like particles that pass through almost everything.

This paper is about a team of scientists (the MINERvA Collaboration) who built a massive detector to catch these neutrinos and study what happens when they smash into atoms. Specifically, they are looking at a specific type of crash called "quasielastic-like," where a neutrino hits a nucleus and knocks out some particles (like protons), leaving the rest of the nucleus intact but shaken up.

Here is the story of their investigation, broken down simply:

The Two Different "Hammers"

To test their theories, the scientists didn't just use one beam of neutrinos. They used two different "hammers" to hit the target:

1. The Low Energy Beam: This beam is like a gentle tap. The neutrinos in it have an average energy of about 3 GeV.
2. The Medium Energy Beam: This beam is a heavy swing. The neutrinos here are about twice as energetic, averaging 6 GeV.

The scientists wanted to see if their "instruction manual" (the computer models they use to predict what happens) worked the same way for both the gentle tap and the heavy swing.

The Mystery of the "Missing Energy"

When a neutrino hits an atom, it's supposed to knock out specific particles. If you measure the speed and direction of the outgoing particles, you should be able to calculate exactly how much energy the incoming neutrino had. It's like a perfect billiard game where you know the cue ball's speed by looking at where the other balls go.

However, atoms are messy. Inside the nucleus, particles are bound together, and when a crash happens, things get complicated:

• Some energy might be swallowed by the nucleus itself.
• Some particles might get stuck or absorbed before they can escape.
• Sometimes, a particle that should have been a proton comes out as a neutron (which is invisible to their detectors).

This "missing" or "invisible" energy makes it hard to know how fast the original neutrino was going. This is a huge problem for experiments trying to study neutrino oscillations (how neutrinos change flavors), because if you don't know the starting energy, you can't measure the change accurately.

The Investigation: Checking the Manual

The scientists measured the crash debris in both the Low Energy and Medium Energy beams. They looked at three things for every crash:

1. How fast the muon (the neutrino's "sibling") was going sideways.
2. How fast it was going forward.
3. The total energy of all the visible protons that flew out.

They compared their real-world data against the predictions from their computer models (specifically a program called GENIE).

The Findings: The Models Got It Wrong

The results showed a clear mismatch between the real world and the computer models:

• The "Over-estimation" Problem: The computer models predicted that there would be more high-energy debris than what the scientists actually saw. It's as if the model thought the crash was much more violent than it actually was.
• The "Invisible" Culprit: The models seemed to overestimate how often particles get absorbed or "swallowed" by the nucleus (Final State Interactions). They thought protons and pions (another type of particle) were bouncing around and getting stuck more often than they really were.
• It's Not Just About Speed: Interestingly, the error didn't change much just because the beam energy changed from 3 GeV to 6 GeV. The mistake was consistent across both beams. This suggests the problem isn't with how the models handle the speed of the neutrino, but rather how they handle the messiness inside the nucleus (the momentum transfer).

The "Double Ratio" Trick

To prove this, the scientists used a clever trick. They took the ratio of the Low Energy data to the Medium Energy data, and then divided that by the ratio of the models for those same beams. This "Double Ratio" acts like a magnifying glass.

If the models were perfect, this ratio would be a flat line at 1.0. Instead, the line dipped below 1.0 in specific areas. This confirmed that the models were predicting too many events where particles got absorbed, especially when the debris had high energy.

The Conclusion

The paper concludes that while the scientists have a good handle on the general behavior of neutrinos, the current computer models used by major experiments (like DUNE and NOvA) are overestimating how much energy gets lost inside the nucleus during these collisions.

They found that the models need to be tweaked to account for the fact that particles don't get absorbed or "stuck" as often as the software currently thinks. Until these models are fixed, scientists trying to measure neutrino properties might be slightly off in their calculations, much like trying to guess a car's speed based on debris that the computer thinks flew further than it actually did.

In short: The scientists built a better map of the "traffic" inside the atomic nucleus. They found that the current maps (models) are too pessimistic about how much traffic gets stuck, and they need to be updated to match the reality seen in both low and high-energy crashes.

Technical Summary

Technical Summary: Comparisons of Triple-Differential Cross Sections for Quasielastic-like $\nu_\mu$-Hydrocarbon Interactions

Problem and Motivation
Neutrino oscillation experiments rely heavily on charged-current (CC) quasielastic-like (QE-like) scattering events to reconstruct neutrino energy. However, these interactions on nuclear targets are complicated by poorly understood nuclear effects, including bound nucleon motion, short-range multinucleon correlations (2p2h), and final-state interactions (FSI) where produced hadrons undergo rescattering or absorption within the nucleus. These effects can obscure the relationship between the visible final-state energy and the incident neutrino energy. While previous measurements have identified discrepancies between data and interaction models, the dependence of these modeling errors on neutrino energy remains a critical uncertainty. This paper addresses the need to test interaction models across different neutrino energy spectra to determine if mismodeling is a function of neutrino energy or momentum transfer.

Methodology
The MINERvA collaboration analyzed data from two distinct wideband neutrino beams produced by 120 GeV protons striking graphite targets at Fermilab:

1. Low Energy (LE) Beam: Peaks near 3 GeV, with few neutrinos above 6 GeV.
2. Medium Energy (ME) Beam: Peaks near 6 GeV, with few neutrinos above 10 GeV.

Both datasets were collected using the same fine-grained MINERvA detector and the MINOS Near Detector for muon reconstruction. The analysis focuses on CC QE-like events ($\nu_\mu + A \to \mu^- + \text{nucleons} + A'$) where the final state contains only a muon and nucleons. The study measures triple-differential cross sections in terms of:

• Muon transverse momentum ($p_t$)
• Muon longitudinal momentum ($p_{||}$)
• The sum of kinetic energies of all final-state protons ($\Sigma T_p$), representing the calorimetrically visible recoil energy.

The analysis employs a simultaneous joint fit to signal and background-dominated samples (categorized by Michel electrons and isolated clusters to identify $\pi^+$ and $\pi^0$) to constrain background levels. Background-subtracted event rates are unfolded using an iterative technique. The primary reference model is a modified version of the GENIE event generator (v2.8.4 for LE, tuned to be equivalent to v2.12.6 for signal processes), incorporating specific MINERvA tunes for pion production and multinucleon (2p2h) enhancements.

Key Contributions and Results
The paper presents a direct comparison of triple-differential cross sections between the LE and ME beams, a novel approach that isolates the energy dependence of nuclear effects.

• Discrepancies in Cross Sections: Significant discrepancies are observed between the data and the MINERvA base model predictions. Specifically, the model overpredicts the cross section strength in the region of high $\Sigma T_p$ (above 200–300 MeV) and low $p_t$. This overprediction is most pronounced in the LE beam for $p_t < 400$ MeV/c and in the ME beam for $p_t < 330$ MeV/c.
• FSI Modeling Issues: The data indicates an overestimation of final-state interaction (FSI) strengths in the simulation. This manifests as an overprediction of events where protons knock out neutrons (resulting in "invisible" energy loss) and an overprediction of pion production followed by absorption.
• Energy Dependence: A critical finding is that the discrepancies between data and prediction are largely consistent across the two different beam energies when viewed as a function of $p_t$ and $\Sigma T_p$. The double ratio of (Data/Model)$_{LE}$ to (Data/Model)$_{ME}$ remains consistently below unity in regions dominated by pion absorption and high $\Sigma T_p$. This suggests that the mismodeling is primarily a function of momentum transfer and the specific nuclear processes (like pion absorption) rather than a strong function of the incident neutrino energy.
• Model Comparisons: The study compares the data against various configurations of GENIE (including settings for DUNE), NEUT, and NuWro. None of the alternative models successfully reproduce the shape of the cross section at low $p_t$ or the specific energy dependence observed in the double ratios. While some models perform better at intermediate kinematics, they fail to resolve the core discrepancies in the QE-like region.

Significance
The paper concludes that the ability to model the visible energy distribution of neutrino interactions is currently limited by the treatment of final-state interactions and pion absorption, rather than by the neutrino energy spectrum itself. By demonstrating that the mismodeling persists across a factor-of-two difference in beam energy, the results provide a stringent benchmark for current and future neutrino event generators. The findings imply that improvements to oscillation analyses must focus on refining the modeling of intranuclear processes (specifically FSI and pion absorption) to correctly infer neutrino energy from quasielastic-like samples, rather than assuming the errors scale simply with beam energy. These results serve as a direct test for the interaction models used to infer neutrino energies in oscillation experiments.