Signal selection and model-independent extraction of pionless charged-current muon neutrino cross section using double-differential kinematic imbalance observables on carbon and oxygen with the T2K experiment

Technical Summary: Signal Selection and Model-Independent Extraction of Pionless Charged-Current Muon Neutrino Cross Section

Problem Statement
Current and future accelerator-based neutrino experiments, such as T2K, NOvA, Hyper-Kamiokande, and DUNE, aim for precision measurements of neutrino oscillation parameters. However, the dominant systematic uncertainty in these measurements arises from the modeling of neutrino–nucleus interactions. Specifically, "nuclear effects"—including initial nucleon states, nucleon correlations, and final-state interactions (FSI)—distort the reconstructed neutrino energy spectrum, potentially biasing oscillation parameter extraction. Existing interaction models often fail to adequately describe data across various kinematic regimes. To address this, there is a critical need for high-precision, model-independent cross-section measurements that can isolate and constrain these nuclear effects.

Methodology
This analysis presents the first joint measurement of muon neutrino charged-current interactions with zero pions and at least one proton ($\nu_\mu$ CC0$\pi$Np) on carbon and oxygen targets using the T2K Near Detector 280 (ND280). The study utilizes data collected between 2010 and 2017, corresponding to $11.61 \times 10^{20}$ protons on target (POT).

• Signal Definition and Selection: The signal is defined as interactions producing one muon, no pions, and at least one reconstructed proton originating from the interaction vertex. The analysis employs a sophisticated event selection algorithm applied to the fiducial volumes of the Fine-Grained Detectors (FGD1 and FGD2). The sample is subdivided based on detector sub-components (TPC vs. FGD tracking) and target material (FGD2 is further split into "FGD2X" and "FGD2Y" to enhance oxygen and carbon purity, respectively).
• Kinematic Imbalance (KI) Observables: To enhance sensitivity to nuclear effects, the cross-section is measured differentially in two double-dimensional spaces using KI observables:
  1. $\delta p_T$ vs. $\delta \alpha_T$: Transverse momentum imbalance and the transverse boosting angle.
  2. $p_N$ vs. $\cos \theta_\mu$: Inferred initial nucleon momentum and the muon scattering angle.
     These observables exploit correlations between the outgoing lepton and hadrons to probe initial-state motion, multi-nucleon correlations, and FSI.
• Background Control: The dominant backgrounds, primarily $\nu_\mu$ CC1$\pi^+$ and CC1$\pi^0$ interactions where pions are missed, are handled via a data-driven approach. A dedicated control sample enriched in $\nu_\mu$ CC1$\pi^+$ interactions (requiring Michel electrons or identified pion tracks) is used to constrain the background normalization in the fit.
• Extraction Framework: The cross-section is extracted using a template-fit unfolding method with the GUNDAM software. The fit utilizes a binned likelihood function comparing data to Monte Carlo (MC) templates. The fit parameters include unconstrained signal normalization factors for each true observable bin and constrained nuisance parameters for detector effects, neutrino flux, and interaction modeling (CCQE, 2p2h, FSI, SPP, etc.). The extraction is validated through coverage tests and physics pseudo-data fits using alternative interaction models (e.g., GENIE) to ensure model independence.

Key Contributions

• Joint Measurement: This work provides the first simultaneous measurement of $\nu_\mu$ CC0$\pi$Np cross-sections on both carbon and oxygen targets, addressing the specific nuclear composition of the Super-Kamiokande far detector.
• Double-Differential KI Observables: The analysis introduces double-differential measurements in $\delta p_T$–$\delta \alpha_T$ and $p_N$–$\cos \theta_\mu$ spaces. These observables are designed to decouple overlapping nuclear effects, offering enhanced discrimination between initial-state motion, multi-nucleon correlations, and final-state interactions compared to single-variable measurements.
• Model-Independent Extraction: By employing a template fit with unconstrained signal bins and rigorous validation against alternative generators, the analysis extracts cross-sections that are minimally dependent on the specific neutrino interaction model used in the simulation.
• Comprehensive Uncertainty Evaluation: The study includes a detailed evaluation of systematic uncertainties, including detector reconstruction, flux prediction (constrained by NA61/SHINE data), and interaction modeling, utilizing control samples and covariance matrices.

Results
The analysis selected 9,469 $\nu_\mu$ CC0$\pi$Np candidates with an overall signal purity of 74.7%. The extracted double-differential cross-sections reveal significant discrepancies between the data and current neutrino–nucleus interaction models (specifically the NEUT generator used in the simulation).

• Data-MC Discrepancies: The data exhibit an excess of events near the peaks of the $\delta p_T$ and $p_N$ distributions compared to MC predictions. Additionally, the MC tends to overestimate the data for muons produced in the very forward direction ($\cos \theta_\mu \sim 1$).
• Model Performance: The results indicate that current models do not adequately describe the data, particularly in the regions sensitive to nuclear effects. The strong discriminating power of the KI observables is demonstrated by the clear separation of different interaction contributions in the 2D phase spaces.

Significance
The paper concludes that the observed discrepancies highlight a critical need for improved theoretical nuclear modeling within neutrino interaction generators. The strong sensitivity of the KI observables to nuclear effects suggests that these measurements are essential for reducing systematic uncertainties in neutrino oscillation analyses. By providing precise, model-independent cross-section data on carbon and oxygen, this work supports the development of more accurate interaction models, which is a prerequisite for achieving the high-precision goals of current and next-generation neutrino oscillation experiments.