Muon Neutrino Interactions on Water

• The paper investigates key muon neutrino interactions on water by examining charged-current quasi-elastic scattering through water Cherenkov and liquid scintillator techniques.
• It details systematic energy reconstruction methods and advanced detector designs that optimize particle identification and reduce background interference in oscillation experiments.
• Measured cross sections on water are compared with hydrocarbon targets, supporting refined nuclear modeling and improved sensitivity in nonstandard interaction searches.

Muon neutrino interactions on water play a central role in contemporary neutrino physics, particularly in the context of oscillation experiments, nonstandard interaction searches, and precision modeling of nuclear effects. The deployment of water-based detectors—often in off-axis or long-baseline configurations—enables systematic measurements of both inclusive and exclusive muon neutrino cross sections, energy reconstruction performance, background mitigation strategies, and inter-material comparisons critical for next-generation oscillation analyses.

1. Principles of Muon Neutrino Interactions in Water

Muon neutrinos ($\nu_\mu$) primarily undergo charged-current (CC) quasi-elastic (QE) scattering when interacting with nuclei in water:

$\nu_\mu + n \rightarrow \mu^- + p$

This process occurs predominantly on oxygen nuclei in H$_2$O; in heavy water (D$_2$O), deuterium interactions can be isolated and exploited for flux and nucleon structure measurements (Orden et al., 2017). Water Cherenkov detectors and water-based liquid scintillators detect the products of such interactions via the emission of Cherenkov and/or scintillation light. The Cherenkov technique, utilized by IMB, Kamiokande, and Super-Kamiokande, discriminates between $\mu$-like (sharp rings) and $e$-like (fuzzy rings) topologies, relying on particle velocity thresholds and ring-pattern reconstruction (Yanagisawa et al., 2010, Li et al., 15 Aug 2025).

Energy reconstruction for QE events leverages lepton kinematics. For muons, the reconstructed energy is typically computed as:

$$E_\nu^{\text{QE}} = \frac{2(M_n - E_b)E_\mu - (E_b^2 - 2M_nE_b + \Delta M^2)}{2(M_n - E_b - E_\mu + p_\mu \cos\theta_\mu)}$$

where $M_n$ is the neutron mass, $E_b$ effective binding energy, $E_\mu$ and $p_\mu$ are muon energy and momentum, $\theta_\mu$ is the scattering angle, and $\Delta M^2 = M_n^2 - M_p^2 + m_\mu^2$ (Coloma et al., 2013). For D$_2$O targets, kinematic optimization (e.g., $y=0$ scaling variable) suppresses oxygen backgrounds by an order of magnitude, allowing the deuterium contribution to dominate and enabling clean incident energy reconstruction (Orden et al., 2017).

2. Experimental Techniques and Detector Technologies

Recent advances exploit modular water targets and segmented calorimeters for enhanced spatial and particle identification resolution. The WAGASCI-BabyMIND detector integrates 3D scintillator grids immersed in water with magnetized downstream tracking, enabling high-fidelity separation of CC0$\pi^{\pm}$ events (muon-neutrino CC interactions with no charged pions) (Abe et al., 9 Sep 2025). The ND280 detector at T2K employs interleaved water and scintillator modules, and Time Projection Chambers (TPCs), to reconstruct kinematics and isolate water-specific signals through water-in/water-out subtraction (Yuan, 2016, Collaboration et al., 2017).

Water-based liquid scintillator (WbLS), featuring $>$80% water by mass and 1 cm$^3$ optical segmentation, substantially lowers detection thresholds and improves spatial granularity for final-state particle tracking (Li et al., 15 Aug 2025). Orthogonal wavelength-shifting fibers and SiPM readout are used to acquire both Cherenkov and scintillation signals. Monte Carlo studies and cosmic ray calibration validate the performance, yielding light yields of $\sim$6 p.e./channel/MIP for WbLS and crosstalk levels $\sim$2%.

Nuclear emulsion detectors, as employed by the NINJA experiment, provide submicron resolution across thin water and iron layers, allowing reconstruction of protons down to 200 MeV/$c$ and charged pions below 50 MeV/$c$ (Hiramoto et al., 2020). Multiple Coulomb scattering techniques, likelihood PID algorithms, and cross-detector matching underpin the identification and kinematic reconstruction of all charged final-state particles.

3. Cross Section Measurements and Model Comparisons

Precision cross section measurements on water span a wide energy range (0.6–1.5 GeV) and target configurations. Experimental results include:

Target	$\sigma_{\text{CC}}$ [cm$^2$/nucleon]	Energy	Reference
H$_2$O	$(1.44 \pm 0.21) \times 10^{-39}$	$0.7$ GeV	(Abe et al., 9 Sep 2025)
CH	$(1.26 \pm 0.18) \times 10^{-39}$	$0.7$ GeV	(Abe et al., 9 Sep 2025)
H$_2$O	$(0.840 \pm 0.010 ^{+0.10}_{-0.08}) \times 10^{-38}$	$1.5$ GeV	(Abe et al., 2019)
CH	$(0.817 \pm 0.007 ^{+0.11}_{-0.08}) \times 10^{-38}$	$1.5$ GeV	(Abe et al., 2019)

The water to hydrocarbon cross section ratios are consistently near unity (e.g., $1.028 \pm 0.016 \pm 0.053$) (Abe et al., 2019, Kleykamp et al., 2023), confirming model robustness across materials in the QE-like regime. Heavy nuclei (Fe, Pb) show enhanced cross sections and nontrivial dependence on transverse momentum, which are not reproduced by current generators (GENIE hA/hN, NEUT, NuWro) (Kleykamp et al., 2023).

Differential cross sections for CC1$\pi^+$ (single charged pion) production on water at T2K ND280 are reported as $$\langle \sigma \rangle_\phi = 4.25 \pm 0.48 (\text{stat}) \pm 1.56 (\text{syst}) \times 10^{-40}$$ cm$^2$/nucleon in a restricted phase space, consistent with NEUT predictions and $\sim2\sigma$ below GENIE values (Collaboration et al., 2016). Double-differential results in $(p_\mu, \cos\theta_\mu)$ are systematically unfolded using Bayesian or binned likelihood methods, with penalties or regularization applied for physical smoothness (Collaboration et al., 2017, 1908.10249).

4. Nuclear Effects, Final State Interactions, and Event Generators

Detection and interpretation of muon neutrino interactions in water require robust modeling of nuclear effects. Standard event generators (GENIE, NEUT, GiBUU, NuWro) implement the impulse approximation with relativistic Fermi Gas (RFG), Local Fermi Gas, or spectral function approaches, accounting for modifications from binding energy, Fermi motion, and multi-nucleon processes (e.g., 2p2h, MEC) (Coloma et al., 2013). Final state interactions (pion absorption, nucleon re-scattering) can "migrate" non-QE events into QE-like samples, affecting neutrino energy reconstruction and oscillation parameter extraction.

Migration matrices $M(E^{\text{rec}}, E^{\text{true}})$ and two-dimensional smearing matrices are employed to model the misreconstruction of true kinematics due to nuclear effects and detector resolution. Discrepancies between generators and data, especially in heavy nuclei and charged pion multiplicities, signal the need for improvements in FSI, intranuclear cascade models (GENIE hA, hN), and the treatment of multi-hadron processes (Kleykamp et al., 2023, Hiramoto et al., 2020).

5. Backgrounds and Systematic Uncertainties in Water-Based Detectors

Both beam-induced and cosmic-induced backgrounds impact muon neutrino measurements in water. Neutral current (NC) events producing $\pi^0$ are a dominant background for $\nu_e$ appearance searches, as their two-photon decays can mimic $e$-like rings (Yanagisawa et al., 2010). POLfit algorithms and multivariate analyses (e.g., discrimination using reconstructed invariant mass, likelihood ratios) are employed for $\pi^0$ rejection, preserving $\nu_e$ signal efficiency.

Stopped cosmic muons (predominantly at shallow depths) contribute low-energy neutrino fluxes via decay and nuclear capture. In a detector at $d=1000$ m, these produce $\nu_\mu$ and $\bar{\nu}_\mu$ fluxes at $3.7\%$ and $6.2\%$ of the atmospheric rates, respectively, with strong geographical and directional dependence—most events originate within $200$ km and arrive nearly horizontally. The $\bar{\nu}_e$ flux is sensitive to the local rock/water mixture via the muon decay probability ($81.56\%$ in water, $60.65\%$ in rock) (Guo, 2018).

Systematic uncertainties are dominated by flux normalization (driven by hadron production), detector simulation (geometry, mass, tracking), and model parameters (axial mass, multinucleon rates). Subtraction techniques (water-in/water-out run comparison) and control sidebands are standard approaches for isolating signal and controlling backgrounds (Yuan, 2016, Collaboration et al., 2017).

6. Implications for Oscillation Physics and Nonstandard Interactions

High-precision cross section measurements on water are essential for minimizing systematic uncertainties in oscillation parameter extraction, notably $\theta_{13}$, $\theta_{23}$, $\delta_{CP}$, and mass hierarchy (Yanagisawa et al., 2010). The consistency of water cross sections with CH and C enables reliable near-far detector extrapolation, crucial in long-baseline experiments (T2K, Hyper-K, DUNE) (Abe et al., 2019, Kleykamp et al., 2023).

Nonstandard interaction (NSI) constraints have been obtained via accelerator and atmospheric neutrino data, with current limits on $\varepsilon_{\mu\mu}^{qP}$ at the few $\times 10^{-2}$ level (Escrihuela et al., 2011). MINOS results for flavor-changing NSI ($\epsilon_{\mu\tau}$) yield $\epsilon = -0.187 \pm 0.16$ (Isvan, 2011). High-energy muon colliders provide complementary sensitivity to muonic NSIs via processes such as $\mu^+ \mu^- \rightarrow \nu \overline{\nu}\gamma$, with projected $\epsilon$ bounds at the $1.5 \times 10^{-4}$ level for $\tau$-flavor channels (Jana et al., 2023).

7. Future Directions and Detector Optimization

With increasing demands for percent-level accuracy in neutrino-nucleus interaction modeling, detector innovation continues. The adoption of highly segmented WbLS modules (Li et al., 15 Aug 2025) and magnetized tracking calorimeters (BabyMIND) (Abe et al., 9 Sep 2025) facilitates comprehensive final-state reconstruction, including low-energy protons and complex topologies. Nuclear emulsion technology is being expanded for higher statistics and improved multi-hadronic detection (Hiramoto et al., 2020).

Consequent improvements in MC generator modeling, such as the refinement of migration matrices and better treatment of multi-nucleon effects, will further reduce systematic uncertainties. Simultaneous measurements on multiple targets (CH, C, Fe, Pb, H$_2$O) over a wide kinematic range set benchmarks for cross-material nuclear modeling (Kleykamp et al., 2023), while optimizing detector composition (maximizing water fraction, minimizing other nuclei) aligns experimental results closely with theoretical expectations for future water Cherenkov and scintillator-based oscillation experiments.

---

In sum, systematic paper of muon neutrino interactions on water—spanning advanced detector technologies, precision cross section measurements, upgraded event generators, and comprehensive background control—is foundational for next-generation oscillation physics and the search for physics beyond the Standard Model. The field continues to progress via coordinated experimental campaigns, rigorous detector simulation, and cross-disciplinary theoretical advances.