Phenomenology of different cross-section models at DUNE

Technical Summary: Phenomenology of Different Cross-Section Models at DUNE

Problem Statement
The precise determination of neutrino oscillation parameters—specifically the CP-violating phase $\delta_{CP}$, the atmospheric mixing angle $\theta_{23}$, and the mass ordering ($\Delta m^2_{32}$)—is contingent upon the accurate reconstruction of neutrino energy on an event-by-event basis. This reconstruction relies heavily on theoretical models of neutrino-nucleus interactions. In the energy range relevant to the Deep Underground Neutrino Experiment (DUNE) (0.5–5 GeV), interactions are dominated by quasi-elastic (QEL) scattering and resonance (RES) production. However, the nuclear medium introduces complex effects such as Fermi motion, Pauli blocking, multinucleon correlations (2p2h), and final state interactions (FSI), leading to significant modeling uncertainties. While the DUNE Technical Design Report (TDR) adopted specific cross-section tunes (Valencia for QEL and Rein–Sehgal for RES), the impact of alternative, potentially more accurate theoretical models on the experiment's physics sensitivity remains to be fully quantified.

Methodology
The authors utilize the GENIE neutrino event generator to simulate the DUNE far detector (four 17-kton Liquid Argon Time Projection Chamber modules) over a 6.5-year run in both neutrino and antineutrino modes. The study isolates the impact of interaction modeling by varying only the QEL and RES cross-section models while keeping Deep Inelastic Scattering (DIS) and 2p2h contributions fixed to the DUNE TDR configuration.

The study compares the following model configurations:

• QEL Models:
  • Valencia: The model used in the DUNE TDR, incorporating Local Fermi Gas and Random Phase Approximation (RPA).
  • Llewellyn-Smith (LS): A formalism using Lorentz-invariant form factors with a dipole axial mass parameterization.
  • HF-CRPA: Hartree–Fock Continuum Random Phase Approximation, which provides a microscopic description of nuclear excitations and long-range correlations, interpolated with SuSAv2 for higher energies.
• RES Models:
  • Rein–Sehgal (RS): The model used in the DUNE TDR, based on the Feynman–Kislinger–Ravndal framework.
  • Berger–Sehgal (BS): An improved version of RS that includes updated resonance parameters, non-resonant background terms, and explicit lepton-mass corrections.

The analysis employs the standard Poisson log-likelihood approach with the pull method for systematic uncertainties. Sensitivities are evaluated for CP violation discovery, mass ordering determination, $\theta_{23}$ octant resolution, and the precision of $\theta_{23}$ and $\Delta m^2_{32}$.

Key Contributions and Results
The paper provides a comparative analysis of cross-section model strengths and their subsequent effect on DUNE's oscillation sensitivities.

1. Cross-Section Strength:

   • In the QEL region, the DUNE tune (Valencia) exhibits the strongest cross-section, followed by HF-CRPA and LS.
   • In the RES region, the Berger–Sehgal (BS) model provides the strongest cross-section, followed by RS and the DUNE tune.
   • Since the DUNE flux peaks in the RES-dominated region (around 2.5 GeV), the total cross-section strength is determined primarily by the RES model. Consequently, the HF-CRPA + BS combination yields the highest total cross-section strength, while the standard DUNE tune (Valencia + RS) yields the weakest strength among the configurations tested.

2. Event Spectra:

   • The HF-CRPA + BS configuration predicts a significant increase in signal events compared to the DUNE tune. Table III indicates an increase in signal yields ranging from 27.6% to 37.4% across different channels (e.g., $\nu_\mu$ disappearance and $\nu_e$ appearance).

3. Oscillation Sensitivities:

   • CP Violation and Mass Ordering: The HF-CRPA + BS model improves the sensitivity to CP violation and mass ordering by approximately 25–30% compared to the DUNE tune. For instance, at $\delta_{CP} \approx 110^\circ$, the $\Delta\chi^2$ for CP violation increases from 78.01 (DUNE tune) to 100.96 (HF-CRPA + BS), a 29.4% improvement.
   • Octant Sensitivity: Similar improvements of 25–25.4% are observed for $\theta_{23}$ octant sensitivity.
   • Parameter Precision: The precision for the atmospheric parameters improves by 15–20%. Specifically, the 3$\sigma$ allowed interval width for $\sin^2\theta_{23}$ is reduced by 19.9%, and for $\Delta m^2_{32}$ by 14.9%.

Significance and Claims
The authors claim that the selection of cross-section models is a critical factor in the physics reach of long-baseline experiments. The study demonstrates that nuclear modeling in the few-GeV QEL–RES transition region can modify DUNE's oscillation sensitivities by roughly 15–30%.

The paper concludes that accurate and systematically validated cross-section descriptions are essential for precision measurements. The large variations in sensitivity observed due to different theoretical models serve as an indirect estimation of the current systematic uncertainties associated with cross-section modeling. The authors assert that sustained advancement in nuclear interaction models, specifically the adoption of frameworks like HF-CRPA and BS where appropriate, is required to fully exploit the physics potential of DUNE.

Note: The authors explicitly state that this work represents their views and not necessarily those of the DUNE Collaboration, and that a comparative analysis using the current (post-TDR) DUNE tune will be performed in a separate study.