Characterising the role of final state interactions on neutrino energy estimation in the DUNE and Hyper-K era

This paper demonstrates that uncertainties in modeling final-state interactions (FSI) significantly impact neutrino energy estimation for DUNE and Hyper-K, with each experiment being sensitive to distinct FSI mechanisms, thereby highlighting the critical need for refined theoretical and experimental approaches to meet future oscillation precision goals.

The Gist

Imagine you are trying to measure the speed of a car by looking at the debris it kicks up after crashing into a wall. If you know exactly how the car hit the wall and how the debris flew, you can work backward to figure out how fast the car was going.

This is essentially what the Deep Underground Neutrino Experiment (DUNE) and Hyper-Kamiokande (Hyper-K) are trying to do. They are giant detectors trying to measure neutrinos—tiny, ghost-like particles that zip through the universe. To understand the secrets of the universe (like why the universe is made of matter instead of antimatter), these experiments need to know the exact energy of the neutrinos hitting them.

However, neutrinos don't just hit a target and stop. They smash into the nucleus of an atom (like oxygen in water or argon in a tank), creating a shower of new particles. These new particles then bounce around inside the atom, hitting other particles before they finally escape the atom and reach the detector. This chaotic bouncing is called Final State Interactions (FSI).

The Problem: The "Bouncy Castle" Effect

The paper argues that these "bounces" are a major headache for scientists.

Think of the atom as a crowded bouncy castle.

1. The Crash: A neutrino crashes into the castle, launching a few kids (particles) into the air.
2. The Bounces: Before those kids can jump out of the castle to be counted by the sensors, they bounce off the walls and other kids.
   • Sometimes a kid gets stuck in a corner (absorbed).
   • Sometimes they knock a loose ball (a neutron) out of the castle that nobody sees.
   • Sometimes they change direction or lose energy.

The scientists in the detector only see the kids who successfully jump out. They try to guess the speed of the original neutrino based on what they see. But because they don't know exactly how the "bounces" inside the castle changed the kids' paths or energy, their guess is often wrong.

The Two Experiments: Different Tools, Different Problems

The paper compares two massive experiments, which use different "tools" to guess the neutrino's energy, and finds they are tripped up by different parts of the bouncy castle.

1. Hyper-Kamiokande (The "Lepton-Only" Detective)

• How it works: This detector is like a pool of water. It mostly looks at the "lepton" (a specific particle like a muon) that flies out of the crash. It ignores the messy debris inside the castle.
• The Weakness: It is very sensitive to pion absorption. Imagine a kid (a pion) who was supposed to jump out but got swallowed by the bouncy castle walls. Because the detector doesn't see this kid, it thinks the crash was less energetic than it really was.
• The Metaphor: It's like trying to guess the speed of a car by only looking at the driver. If the driver gets stuck in the car and doesn't jump out, you might think the car was moving slowly, even if it was speeding.

2. DUNE (The "Total Energy" Accountant)

• How it works: This detector is a tank of liquid argon. It tries to count every bit of energy that comes out, including the debris (protons, pions, etc.). It's like an accountant trying to sum up every penny that leaves the building.
• The Weakness: It is very sensitive to invisible energy loss, specifically neutrons. Neutrons are like ghosts; they leave the castle but don't leave a trace in the detector. If a lot of energy is lost to these invisible ghosts, the accountant thinks the total energy is lower than it actually is.
• The Metaphor: It's like trying to balance a budget, but some of the money is being stolen by invisible pickpockets (neutrons) that you can't see.

The Findings: The Guesswork is Too Rough

The authors ran complex computer simulations (using "event generators" which are like video game engines for particle physics) to see how much these "bounces" mess up the energy calculations.

• The Goal: To measure the universe's secrets, these experiments need to know the neutrino energy with extreme precision—within about 5 to 15 million electron-volts (MeV). That's like needing to measure the speed of a car within a few inches per hour.
• The Reality: The paper found that the uncertainty caused by the "bouncy castle" physics (FSI) is larger than the precision they need.
  • For Hyper-K, not knowing exactly how often pions get absorbed creates an error bigger than the 5 MeV target.
  • For DUNE, not knowing exactly how much energy neutrons steal creates an error bigger than the 15 MeV target.

The Solution: Better Maps and New Measurements

The paper concludes that we cannot just guess how the particles bounce. We need better "maps" of the bouncy castle.

1. Better Models: We need to move beyond simple, semi-classical rules (like "bouncing off a wall") and use more advanced quantum mechanics to understand how particles interact with the nucleus.
2. New Experiments: We need to go to the "source" and measure these interactions directly.
   • For Hyper-K, we need to shoot pions at oxygen to see exactly how often they get absorbed.
   • For DUNE, we need to shoot protons and pions at argon to see exactly how much energy neutrons steal.

In short: The paper warns that if we don't figure out exactly how particles behave inside the atomic nucleus (the "bouncy castle"), the two biggest neutrino experiments in the world might be too confused by the debris to solve the mysteries of the universe they are built to find. They need to control the "bounces" to within a few MeV, but currently, their models are too fuzzy to guarantee that.

Technical Summary

Technical Summary: Characterising the role of final state interactions on neutrino energy estimation in the DUNE and Hyper-K era

Problem Statement
The Deep Underground Neutrino Experiment (DUNE) and Hyper-Kamiokande (Hyper-K) aim to measure neutrino oscillation parameters with unprecedented precision, targeting sub-percent level measurements of mixing angles and the CP-violating phase $\delta_{CP}$. Achieving this requires controlling systematic uncertainties on the neutrino energy scale to the few-MeV level (approximately 5 MeV for Hyper-K and 15 MeV for DUNE). A primary source of uncertainty in reconstructing neutrino energy is the modelling of Final State Interactions (FSI)—the reinteractions of hadrons produced in neutrino-nucleus scatters with the residual nuclear medium. Current simulations predominantly rely on semi-classical intranuclear cascade (INC) models, which may not fully capture the complexity of nuclear effects. This work investigates whether plausible variations in FSI modelling introduce energy estimation biases that exceed the precision requirements necessary for the next generation of long-baseline (LBL) experiments.

Methodology
The authors utilize state-of-the-art neutrino interaction Monte Carlo event generators—NuWro (v25.03.1), GENIE (v3.02.00), and NEUT (v6.1.3)—to simulate neutrino interactions on water (for Hyper-K) and argon (for DUNE) targets. The study focuses on charged-current (CC) interactions within the few-GeV energy regime, covering CC quasi-elastic (CCQE), multi-nucleon (CCnpnh), resonant pion production (CCRPP), and deep inelastic scattering (CCDIS) channels.

Two distinct approaches to FSI modelling are compared:

1. Semi-classical Intranuclear Cascades (INC): Used by NuWro, GENIE (hA2018, hN2018, INCL, G4BC), and NEUT. These models transport hadrons through the nucleus in discrete steps, probabilistically determining scattering, absorption, or charge exchange.
2. Microscopic Quantum Mechanical Calculations: Implemented in NEUT via the Energy-Dependent Relativistic Mean Field (ED-RMF) model. This approach calculates hadron currents using bound- and scattered-state wavefunctions in a relativistic nuclear potential, encoding elastic FSI effects consistently with the cross-section calculation.

The study evaluates the performance of the specific energy estimators used by each experiment:

• Hyper-K: Uses a kinematic estimator ($E^{QE}_{\nu}$) based on lepton kinematics, assuming a CCQE interaction on a stationary nucleon.
• DUNE: Uses calorimetric estimators ($E^{avail}_{\nu}$ and $E^{had}_{\nu}$) that sum the visible energy deposits of leptons, protons, and pions, accounting for kinetic energy and mass energy where appropriate.

The analysis quantifies the bias (difference between estimated and true neutrino energy) under various conditions: without FSI, with standard INC, with variations in pion absorption probability ($\pm 31\%$), variations in nucleon mean free path ($\pm 30\%$), switching between different INC models, and toggling the microscopic nuclear potential (ED-RMF vs. RPWIA).

Key Contributions and Results
The paper demonstrates that FSI modelling introduces uncertainties in neutrino energy estimation that are at or above the precision levels required for DUNE and Hyper-K oscillation sensitivities.

• Differential Impact on Experiments: The two experiments are sensitive to different aspects of FSI due to their distinct energy estimators.

  • Hyper-K: The kinematic estimator is largely blind to changes in hadron kinematics or multiplicities that do not alter the event topology. The dominant FSI effect is pion absorption, which converts resonant pion production events (where the kinematic estimator is biased) into CC0$\pi$ topologies. Additionally, the inclusion of a microscopic nuclear potential (ED-RMF) significantly reshapes the bias distribution for CCQE interactions, introducing shifts not captured by semi-classical cascades.
  • DUNE: The calorimetric estimators are highly sensitive to the partitioning of hadronic energy between visible (protons, pions) and invisible (neutrons, nuclear binding energy) channels. Variations in the INC model significantly alter the fraction of energy carried away by neutrons and the charged pion multiplicity, leading to substantial shifts in the energy estimation bias.

• Magnitude of Uncertainties:

  • Variations in pion absorption probability cause mean bias shifts of up to $\sim 16$ MeV for Hyper-K and $\sim 11$ MeV for DUNE (depending on the estimator).
  • Switching between different INC models in GENIE results in mean bias shifts of up to $\sim 9$ MeV for Hyper-K and $\sim 45$ MeV for DUNE.
  • The inclusion of the microscopic nuclear potential (ED-RMF) shifts the median bias by $\sim 7$ MeV for Hyper-K, a significant effect despite a smaller shift in the mean.
  • These shifts often exceed the target control levels of 5 MeV (Hyper-K) and 15 MeV (DUNE).

• Energy Dependence: The bias is not constant; it grows with neutrino energy. For Hyper-K, this is driven by the rising cross-section of CCnpnh and pion production relative to CCQE above $\sim 0.5$ GeV. For DUNE, higher energy transfers lead to increased neutron emission and pion multiplicities.

• Asymmetry: FSI modelling does not affect neutrino and antineutrino energy estimation symmetrically. For instance, variations in the nucleon mean free path shift the bias in opposite directions for neutrinos and antineutrinos in DUNE, which could complicate the extraction of $\delta_{CP}$ if not properly constrained.

Significance and Claims
The authors claim that the current reliance on semi-classical INC models introduces a "problem to be solved" rather than a settled systematic uncertainty. The results highlight that:

1. FSI Modelling is Critical: Plausible variations in FSI models generate energy scale uncertainties comparable to or larger than the precision goals of DUNE and Hyper-K.
2. Experiment-Specific Sensitivities: Robust constraints cannot be achieved with a single universal model; Hyper-K requires precise modelling of pion absorption and microscopic nuclear potentials, while DUNE requires precise constraints on hadronic energy sharing (specifically neutron production).
3. Need for Dedicated Measurements: The paper argues that controlling these uncertainties requires a coordinated program of theoretical development (extending microscopic treatments beyond CCQE) and dedicated experimental measurements. Specifically, new pion-oxygen scattering data is needed for Hyper-K, and proton/pion-argon scattering data (e.g., from ProtoDUNE) is needed for DUNE to constrain the energy transfer to neutrons.
4. Role of Near Detectors: While the raw model spreads presented are large, the authors note that in a real analysis, Near Detector (ND) constraints will reduce the residual bias. However, the energy dependence of the bias means ND constraints rely on the underlying interaction model to extrapolate to the Far Detector, necessitating robust parameterised uncertainties.

The paper concludes that achieving the ultimate sensitivity of DUNE and Hyper-K depends on bringing FSI modelling uncertainties under control through the coupling of theoretical advances with targeted experimental measurements.