First double-differential measurement of pionless charged-current muon neutrino interactions using kinematic imbalance observables on carbon and oxygen with the T2K experiment

Technical Summary: First Double-Differential Measurement of Pionless Charged-Current Muon Neutrino Interactions on Carbon and Oxygen

Problem and Motivation
Current and future long-baseline neutrino oscillation experiments, such as T2K and Hyper-Kamiokande, rely on precise measurements of neutrino oscillations by comparing observed spectra to theoretical predictions. At sub-GeV energies (~0.6 GeV), the signal is dominated by pionless charged-current (CC0$\pi$) interactions. Standard reconstruction techniques assume quasi-elastic (QE) scattering off a free nucleon at rest; however, nuclear effects—including Fermi motion, multi-nucleon correlations (short/long range), and final-state interactions (FSIs)—violate this assumption. FSIs can absorb pions from production channels, migrating events into the CC0$\pi$ sample and distorting neutrino energy reconstruction.

Existing measurements on oxygen, the primary target for Super-Kamiokande and Hyper-Kamiokande, are scarce and limited to leptonic kinematics, lacking sensitivity to hadronic final states necessary to probe complex nuclear effects. Consequently, T2K oscillation analyses currently extrapolate carbon-based results from the near detector (ND280) to oxygen targets. This extrapolation introduces significant model dependence, with widely used interaction generators predicting carbon-to-oxygen cross-section ratios differing by up to ~10%. To resolve these modeling uncertainties and reduce systematic errors in oscillation parameters ($\theta_{23}$, $\Delta m^2_{32}$, $\delta_{CP}$), direct measurements on multiple targets using kinematic imbalance observables are required.

Methodology
This work presents the first double-differential cross-section measurement of $\nu_\mu$ CC0$\pi$ interactions with at least one final-state proton ($\nu_\mu$ CC0$\pi$Np) on both carbon and oxygen targets. The analysis utilizes data collected by the T2K experiment's ND280 near detector between 2010 and 2017, corresponding to an exposure of $11.61 \times 10^{20}$ protons on target (POT).

• Targets and Detection: The analysis employs two fine-grained scintillator detectors (FGDs) within ND280. FGD1 serves as a carbon target, while FGD2, composed of interleaved plastic scintillator and water layers, provides a mixture of carbon and oxygen targets. Charged particles are tracked by surrounding time projection chambers (TPCs).
• Signal Selection: The signal sample consists of $\nu_\mu$ CC0$\pi$Np interactions within the fiducial volumes of FGD1 and FGD2. Kinematic constraints are applied to the outgoing muon ($0.225 < p_\mu < 10$ GeV/c, $\cos\theta_\mu > -0.6$) and the leading proton ($0.525 < p_p < 1$ GeV/c, $\cos\theta_p > 0.3$) to ensure good detector acceptance. The selected sample contains 9,469 candidates with an estimated composition of 70.8% carbon and 22.3% oxygen interactions. The overall signal purity is 74.6%.
• Kinematic Imbalance (KI) Observables: To disentangle nuclear effects, the measurement is performed as a function of three KI observables:
  1. Transverse momentum imbalance ($\delta p_T$).
  2. Transverse boosting angle ($\delta \alpha_T$).
  3. Inferred initial nucleon momentum ($p_N$), which incorporates longitudinal information derived from energy-momentum conservation.
     The analysis reports double-differential cross sections in two complementary phase spaces: $\delta p_T$–$\delta \alpha_T$ and $p_N$–$\cos\theta_\mu$.
• Analysis Strategy: Cross sections are extracted using a template-fit unfolding method with the GUNDAM software. The fit model includes free normalization parameters to account for data-MC discrepancies. Systematic uncertainties from detector simulation, flux modeling, and interaction modeling are included, with interaction modeling being the dominant source.
• Model Comparison: Measured cross sections are compared against predictions from four neutrino event generators: NEUT v6.1.0, GENIE v3.6.2 (using two configurations: G18 10b and AR23 20i), NuWro v25.03.1, and GiBUU v2025p3. These models employ various approaches for nucleon initial states (Spectral Function vs. Local Fermi Gas), multi-nucleon interactions (Valencia vs. SuSAv2), and FSIs (Intranuclear Cascade vs. transport theory).

Key Contributions

• First Joint Measurement: This is the first double-differential measurement of $\nu_\mu$ CC0$\pi$Np cross sections on both carbon and oxygen simultaneously.
• Direct Sensitivity: By measuring both targets, the work provides direct sensitivity to the correlations between carbon and oxygen, a critical ingredient for reducing systematic uncertainties in experiments utilizing multiple target nuclei.
• Nuclear Effect Probing: The use of $\delta p_T$–$\delta \alpha_T$ and $p_N$–$\cos\theta_\mu$ observables allows for the separation of initial-state dynamics (Fermi motion) from final-state interactions and multi-nucleon correlations.
• Oxygen Specifics: The measurement offers a unique probe of nuclear effects in oxygen, a "doubly magic" nucleus, which has been historically under-studied compared to carbon.

Results

• Uncertainties: The measured cross sections exhibit total relative uncertainties ranging from 15% to 80%, dominated by statistical fluctuations (9%–70%). Among systematic sources, neutrino-nucleus interaction modeling contributes 8%–30%.
• Model Performance:
  • NEUT and NuWro: These models, which utilize the Spectral Function (SF) ground state, the Valencia model for 2p2h interactions, and cascade-based FSIs, show the best overall agreement with the data, yielding the highest p-values across the measured phase spaces.
  • GENIE and GiBUU: These generators exhibit larger tensions with the data, particularly for carbon. However, the GENIE AR23 20i configuration (incorporating short-range correlations and the SuSAv2 model) achieves a better p-value (~0.13) in the $p_N$–$\cos\theta_\mu$ space compared to its G18 10b counterpart.
  • GiBUU Specifics: GiBUU accurately describes the high-angle region ($\delta \alpha_T > 135^\circ$) where FSIs are prominent but fails to capture the low-$\delta \alpha_T$ region dominated by CCQE interactions, likely due to an underestimated $\delta p_T$ bulk.
• Discrepancies: All tested generators under-predict the data in the intermediate $\delta p_T$ region (0.2–0.5 GeV/c) for carbon and show similar, though less pronounced, deficits for oxygen in specific angular regions. A comparable deficit appears in the intermediate $p_N$ range (0.2–0.4 GeV/c) for forward-going muons. These regions are sensitive to short-range correlations (SRCs) and multi-nucleon interactions (npnh), suggesting current implementations of these processes are insufficient. Additionally, for oxygen, data shows a higher cross-section near the $p_N$ peak at large muon scattering angles, indicating a need for refined treatment of the initial nuclear state in this phase space.

Significance
The paper claims that these results provide a novel and highly sensitive probe of nuclear effects, including nucleon initial-state motion, multi-nucleon interactions, and FSIs. The joint measurement offers a direct test of the unified modeling of neutrino-nucleus scattering on carbon and oxygen, which is directly relevant to the physics programs of T2K and Hyper-Kamiokande. The findings highlight specific directions where improvements in neutrino–nucleus interaction modeling are necessary, particularly regarding the description of SRCs and multi-nucleon interactions. While the measurement is currently limited by statistical uncertainties, the methodology and insights established here lay the groundwork for more precise studies of nuclear effects using future T2K data from the upgraded ND280 detector.