Exclusive Hadron Observables in Neutrino Induced $2p2h$ Multinucleon Knockout

This paper investigates exclusive hadron observables in neutrino-induced $2p2h$ multinucleon knockout by comparing kinematic variables from the Valencia model with current event generator treatments and nuclear re-scattering effects, while assessing their detectability in present and future long-baseline neutrino experiments.

The Gist

Imagine you are trying to figure out how a billiard ball was hit, but you can only see the cue ball rolling away. You have to guess the force and angle of the hit based on that single ball. This is essentially what neutrino physicists have been doing for decades. They shoot invisible particles (neutrinos) at atomic nuclei and watch the "cue ball" (a muon) fly off, trying to reconstruct the entire collision.

However, the paper you provided suggests that this "single ball" view is missing a huge part of the story. It turns out that sometimes, the neutrino doesn't just hit one ball; it hits a pair of balls that are holding hands inside the nucleus.

Here is a simple breakdown of what this paper is about, using everyday analogies.

1. The Problem: The "Two-Person Dance"

In the past, scientists used a simplified model (called "inclusive") to predict what happens when a neutrino hits an atom. They assumed that if a neutrino hits two nucleons (protons or neutrons) at once, those two nucleons would fly out like a perfectly synchronized dance duo, sharing the energy equally and moving in opposite directions.

The Reality: The paper argues that this is like assuming two people jumping off a diving board will always jump with the exact same force. In reality, one person might do a big leap while the other just gets a little push. The energy isn't shared equally. One nucleon gets hit hard by the neutrino (the "leader"), while the other gets a secondary push from the first one (the "follower").

2. The New Tool: The "Exclusive" Camera

The authors developed a new, more detailed model (the "Valencia 2p2h model"). Think of the old model as a blurry security camera that just sees "two people left the room." The new model is like a high-definition 4K camera that sees exactly who pushed whom, how hard they jumped, and the specific angle they took.

They call this "Exclusive" because it looks at every single detail of the event, not just the average result.

3. The Key Discoveries

The paper compares the "blurry" old model with the "HD" new model and finds three major differences:

• The "Leader" vs. The "Follower": In the new model, one nucleon usually carries most of the energy (the leader), while the other is much slower (the follower). The old model assumed they were twins with identical energy.
• The Connection to the Muon: The "leader" nucleon is tightly connected to the path of the outgoing muon (the cue ball). If the muon goes left, the leader goes right. The "follower," however, is a bit of a wanderer; its path is much less predictable and doesn't care as much about where the muon went.
• The "Smearing" Effect (Nuclear Re-scattering): As these particles fly out of the nucleus, they crash into other particles inside the atom, like a pinball bouncing off bumpers. This "smears" the data, making it harder to see the differences. However, the authors found that even after all these crashes, the "Leader" nucleon is still usually faster and more energetic than the "Follower." The old model still thinks they are equal, even after the chaos.

4. Why Does This Matter? (The Detective Work)

Neutrino experiments (like T2K in Japan or DUNE in the US) are trying to solve a cosmic mystery: Why do neutrinos change flavors? To do this, they need to know the exact energy of the neutrino when it hit the detector.

• The Old Way: They guess the energy based on the muon alone. Because the old model assumes the nucleons share energy equally, this guess is often wrong. It's like trying to guess the weight of a suitcase by only weighing the handle.
• The New Way: If detectors can spot both nucleons (the leader and the follower), they can use the new "HD" model to calculate the energy much more accurately. This reduces "systematic errors" (mistakes in the measurement) and helps scientists get a clearer picture of the universe.

5. The Future: Better Detectors

The paper highlights that older detectors were like blindfolded detectives; they could only see the muon. But new, upgraded detectors (like the SuperFGD in the T2K experiment) are like detectives with night-vision goggles and high-speed cameras. They can finally see the protons and neutrons flying out.

The authors are saying: "We have a new, more accurate map of the terrain. Now that we have better cameras (detectors), we need to start using this new map to avoid getting lost."

Summary

• Old View: Neutrinos hit two particles, and they split the energy 50/50. (Too simple).
• New View: Neutrinos hit two particles, but one takes the brunt of the hit, and the other gets a secondary push. (More realistic).
• The Result: This difference changes how we calculate the energy of the neutrino.
• The Goal: By using this new, detailed view with next-generation detectors, scientists can measure neutrino properties with much higher precision, helping us understand the fundamental laws of the universe.

In short, this paper is about upgrading our understanding of neutrino collisions from a "cartoon sketch" to a "photorealistic movie," ensuring that when we look at the data, we aren't missing the most important characters in the scene.

Technical Summary

1. Problem Statement

Neutrino-nucleus interactions involving two-particle-two-hole (2p2h) mechanisms (multinucleon knockout) are a dominant source of uncertainty in neutrino oscillation experiments. While current event generators (e.g., GENIE, NEUT, NuWro) successfully model the inclusive cross-sections of these processes, they rely on simplified kinematic assumptions for the outgoing nucleons.

• The Limitation: Current generators typically assume the two outgoing nucleons are emitted back-to-back in the center-of-mass (CM) frame of the nucleon pair, with symmetric momentum sharing. This "inclusive" approach ignores the specific internal dynamics of the primary interaction vertex (e.g., which nucleon interacts directly with the $W$ boson vs. the meson-exchange partner).
• The Consequence: As next-generation detectors (T2K ND280 upgrade, DUNE, SBND) gain the ability to measure exclusive hadronic final states (detecting individual protons and neutrons), these simplified models may fail to accurately reconstruct neutrino energy or distinguish between interaction channels (1p1h vs. 2p2h), leading to biases in oscillation parameter extraction.

2. Methodology

The authors compare two distinct kinematic treatments for 2p2h interactions using the Valencia model framework:

1. Exclusive Valencia 2p2h Model:

   • Based on a microscopic many-body theory including meson-exchange currents (MEC) and $\Delta$-resonance contributions.
   • Calculates exclusive kinematics by explicitly sampling the initial nucleon momenta and the differential cross-section $d\sigma/(d^3r d^3p_{N1} d^3p_{N2} d^3p'_{N1} d^3p'_{N2} d^4q)$.
   • Distinguishes between the nucleon directly interacting with the $W$ boson (absorbing most momentum) and the accompanying nucleon.
   • Uses fixed neutrino energies (450, 650, and 1000 MeV) to isolate kinematic effects from flux convolution.

2. Inclusive Approach (Standard Generator Treatment):

   • Uses hadron tensor tables to compute cross-sections.
   • Samples initial nucleons from a local Fermi gas.
   • Assumes the two outgoing nucleons are emitted back-to-back in the CM frame with symmetric momentum sharing, then boosted to the lab frame.
   • Lacks information about the specific vertex dynamics.

3. Nuclear Re-scattering (NrS):

   • Both exclusive and inclusive event samples are passed through the NEUT semi-classical intranuclear cascade.
   • This simulates final-state interactions (elastic/inelastic scattering, charge exchange, absorption, secondary knockout) to assess how nuclear medium effects smear the primary kinematic differences.

4. Detector Simulation:

   • Applied detection thresholds mimicking the T2K ND280 SuperFGD upgrade (proton $p > 300$ MeV/c, neutron $E_k > 45-50$ MeV) to evaluate observability.

3. Key Contributions

• Identification of Asymmetry: The paper demonstrates that the exclusive model predicts a significant asymmetry in energy and momentum sharing between the two outgoing nucleons. One nucleon (the "leading" nucleon) carries the majority of the transferred four-momentum, while the other ("subleading") carries significantly less. This is physically motivated by the $W$-boson vertex vs. meson-exchange mechanism.
• Lepton-Hadron Correlations: The study quantifies how the leading nucleon's momentum correlates strongly with the outgoing lepton angle ($\theta_\mu$), whereas the subleading nucleon is largely uncorrelated with the lepton kinematics in the exclusive model. The inclusive model incorrectly predicts symmetric correlations for both nucleons.
• Transverse Kinematic Imbalance (TKI): The authors analyze TKI variables ($\delta p_T, \delta \alpha_T, \delta \phi_T$). They show that the exclusive treatment yields distributions that are more "Quasi-Elastic (QE)-like" (smaller $\delta p_T$) because the leading nucleon balances the lepton momentum, whereas the inclusive model produces broader distributions due to symmetric sharing.
• Robustness against NrS: A critical finding is that the kinematic asymmetry and the preference for a high-momentum leading nucleon survive the nuclear re-scattering cascade, despite the smearing of spectra.

4. Key Results

• Momentum Asymmetry: In the exclusive model, the momentum asymmetry $A(p) = (p'_1 - p'_2)/(p'_1 + p'_2)$ is non-zero and skewed, whereas the inclusive model produces a symmetric distribution centered at zero.
• TKI Distributions:
  • $\delta p_T$: Exclusive treatment shows a pronounced peak at low values (QE-like), while inclusive is broader. This difference persists after NrS.
  • $\delta \phi_T$: Exclusive treatment shows a peak near $0$ (back-to-back in transverse plane), mimicking QE, while inclusive is flatter.
• Detector Impact: Even after applying T2K ND280 detection thresholds, the differences between the exclusive and inclusive treatments remain visible in the leading nucleon spectra and TKI variables.
• Reconstructed Target Momentum: The variable $p^{reco}_{target} = |\vec{p}_\nu - \vec{p}_\mu - \vec{p}_{N_{lead}}|$ shows a narrower distribution for the exclusive model, indicating better momentum balance. The exclusive model also reveals a secondary peak at higher momenta due to $\Delta$-resonance contributions, which is washed out in the inclusive approach.
• Energy Dependence: Discrepancies between the two models grow with increasing neutrino energy (450 $\to$ 1000 MeV), as higher available momenta accentuate the kinematic differences.

5. Significance and Implications

• Model Discrimination: The paper establishes that current and future detectors have the capability to distinguish between simplified inclusive models and realistic exclusive dynamics using hadronic observables.
• Oscillation Physics: Since neutrino energy reconstruction in long-baseline experiments often relies on the assumption of 1p1h kinematics, the mis-modeling of 2p2h kinematics (specifically the asymmetric sharing) can introduce biases in reconstructed neutrino energy, affecting oscillation probability measurements.
• Implementation Challenges: The authors note that implementing the full exclusive Valencia model in event generators is computationally expensive due to the high dimensionality of the phase space. They suggest the need for on-the-fly exclusive samplers or surrogate models (e.g., normalizing flows) to make these calculations feasible for large-scale simulations.
• Future Directions: The work advocates for a program combining full detector simulations, targeted experimental selections (focusing on high lepton angles and multi-nucleon final states), and joint lepton+hadron fits to constrain multinucleon dynamics and reduce systematic uncertainties in oscillation measurements.

In summary, this paper provides a rigorous theoretical foundation for moving beyond inclusive approximations in 2p2h modeling, demonstrating that exclusive kinematic observables offer a powerful new handle to validate nuclear models and improve the precision of neutrino oscillation experiments.