MINOS and MINOS+ Neutrino Experiments
- MINOS and MINOS+ experiments are long-baseline projects that use a two-detector design to precisely measure neutrino oscillation parameters and explore physics beyond the Standard Model.
- Key methodologies include advanced machine learning for event classification and joint likelihood analyses to combine charged-current and neutral current data for robust sterile neutrino and NSI searches.
- Major results feature precise measurements of Δm²₃₂ and θ₂₃, underground muon charge ratios, and stringent limits on invisible neutrino decay, guiding future experimental designs.
The MINOS and MINOS+ experiments are long-baseline accelerator neutrino projects designed to probe core aspects of neutrino physics and search for phenomena beyond the Standard Model. Located at Fermilab and the Soudan Underground Laboratory, these experiments combine a magnetized steel–scintillator tracking calorimeter at both a near site (1.04 km) and a far site (735 km) and employ an intense NuMI beam in several energy configurations. Their scientific program encompasses precision measurements of atmospheric and accelerator neutrino oscillation parameters, searches for sterile neutrinos and non-standard interactions, tests of fundamental symmetries, cosmic ray muon studies, and high-statistics cross section measurements.
1. Experimental Architecture and Beam Configurations
MINOS and MINOS+ utilize a two-detector design which enables direct comparison between unoscillated and oscillated neutrino spectra. The Near Detector (ND) constrains the unoscillated flux and mitigates systematic uncertainties associated with beam modeling and cross-section uncertainties by providing a data-driven calibration for the Far Detector (FD) analysis. Both detectors are magnetized to enable event-by-event charge discrimination—crucial for separating neutrinos and antineutrinos and for conducting CPT tests (Habig, 2010).
NuMI delivers a high-intensity neutrino beam generated by impinging 120 GeV protons on a graphite target, with the resultant secondary mesons (mostly π, K) focused by magnetic horns. Beam configurations varied between MINOS (low-energy peak near 3 GeV for maximal atmospheric oscillation sensitivity) and MINOS+ (medium-energy peak near 7 GeV for extended coverage of higher-energy events and new physics searches) (Evans, 2013).
2. Neutrino Oscillation Physics and Parameter Measurement
MINOS has performed high-precision measurements of the atmospheric mass-squared splitting Δm²₃₂ and the mixing angle θ₂₃. Analyses employ full three-flavor oscillation frameworks, modeling the probability for muon neutrino survival as:
With combined beam and atmospheric data, MINOS+ provides some of the most precise measurements to date: for the normal hierarchy, Δm²₃₂ = 2.40⁺⁰.⁰⁸₋₀.₀₉ × 10⁻³ eV² and sin²θ₂₃ = 0.43⁺⁰.²⁰₋₀.₀₄; for inverted, Δm²₃₂ = 2.45⁺⁰.⁰⁷₋₀.₀₈ × 10⁻³ eV² and sin²θ₂₃ = 0.42⁺⁰.⁰⁷₋₀.₀₃ (Collaboration et al., 2020). Analyses combine charged-current ν_μ disappearance with subleading ν_e appearance (sensitive to θ₁₃ and δ_CP), obtaining competitive constraints and probing the mass hierarchy (Collaboration et al., 2011, Holin, 2012, Nakaya et al., 2015).
3. Sterile Neutrino and Non-Standard Interaction Searches
The two-detector topology and broad energy coverage provide strong sensitivity to sterile neutrino mixing (via a 3+1 framework). MINOS+ applies a two-detector fit using both CC and NC data, sensitive to oscillations induced by a fourth, sterile state with Δm²₄₁ up to ~10 eV². Limits are placed on mixing angles, especially θ₂₄, with exclusion regions in the (sin²θ₂₄, Δm²₄₁) plane surpassing previous constraints over several orders of magnitude (Carroll, 2017, Bay et al., 2020). When combined with external reactor antineutrino disappearance (Daya Bay, Bugey-3), MINOS+ exclusions close nearly all LSND/MiniBooNE-favored space below Δm²₄₁ ≈ 5 eV² at 90% CLₛ.
Non-standard neutrino interactions (NSI), both vector (affecting matter propagation) and axial (modifying scattering cross sections), are tested. Neutral current data of MINOS/MINOS+ explicitly constrain axial NSI parameters ε{Aq}_{αβ}—world-leading limits on ε{Aq}_{eτ} and ε{Aq}_{ττ} are achieved by leveraging spectral distortions and flavor composition in NC samples (Abbaslu et al., 2 Sep 2025). The case of isospin singlet couplings, ε{Au}_{ττ} = ε{Ad}_{ττ}, theoretically motivated but previously unconstrained, is now limited to O(0.3).
4. Advanced Analysis Techniques and Data Acquisition
Event selection and reconstruction utilize machine learning methods: k-Nearest Neighbor for CC event classification, Library Event Matching (LEM) and neural networks for background separation in the ν_e appearance channel (Nakaya et al., 2015). Oscillation parameter extraction employs joint binned likelihoods over multiple channels and energy bins, with systematics handled by profile likelihood or covariance matrices. The data acquisition system was upgraded for MINOS+, transitioning to gigabit Ethernet TCP/IP, MVME5500 VME crate processors, and modular multi-core Linux servers—yielding a threefold increase in throughput to 800 Mb/sec and substantially more robust, partitionable operation (Badgett et al., 2015).
5. Special Topic Measurements: Cosmic Rays and Invisible Neutrino Decay
MINOS provided the first direct underground measurement of the atmospheric muon charge ratio at TeV energies, finding an underground value of N_{μ+}/N_{μ-} = 1.374 ± 0.004(stat.)⁺⁰.⁰¹²₋₀.₀₁₀(sys.), and a surface energy-independent ratio in 1–7 TeV. The charge ratio rise at lower energies is explained by increased kaon decay contributions, constraining models for cosmic-ray induced neutrino and muon fluxes (0705.3815). These results are essential for calibrating atmospheric background predictions for underground detectors.
MINOS/MINOS+ have also achieved leading constraints on invisible neutrino decay. By incorporating an exponential damping term into the oscillation Hamiltonian (H_D), and using NC deficit sensitivity to invisible decay channels, the combined data yield τ₃/m₃ ≥ 2.4×10–11 s/eV at 90% CL—an order-of-magnitude better than previous bounds (Ternes et al., 25 Jan 2024).
6. Impact and Legacy in Precision Neutrino Physics
Cumulatively, MINOS/MINOS+ have anchored the global neutrino oscillation parameter landscape—attaining precision on Δm²₃₂ and θ₂₃, determining non-maximal mixing, testing CPT symmetry via separate neutrino and antineutrino samples, and constraining appearance channels. Robust null results for sterile neutrino and NSI scenarios guide the interpretation of anomalous signals in other experiments toward more complex models. The experimental methodologies and data analysis architectures pioneered have informed the design of NOνA and DUNE, enabling the next generation of precision neutrino investigations.
Summary Table: Key Measurement Highlights
| Parameter/Feature | Result/Constraint | Source |
|---|---|---|
| Atmospheric mass splitting Δm²₃₂ | N: 2.40⁺⁰.⁰⁸₋₀.₀₉ × 10⁻³ eV²; I: 2.45⁺⁰.⁰⁷₋₀.₀₈ | (Collaboration et al., 2020) |
| Mixing angle θ₂₃ | N: 0.43⁺⁰.²⁰₋₀.₀₄; I: 0.42⁺⁰.⁰⁷₋₀.₀₃ | (Collaboration et al., 2020) |
| Muon charge ratio, deep (TeV) | N_{μ+}/N_{μ-} = 1.374 ± 0.004⁺⁰.⁰¹²₋₀.₀₁₀ | (0705.3815) |
| Invisible neutrino decay, τ₃/m₃ | ≥ 2.4 × 10⁻¹¹ s/eV (90% CL) | (Ternes et al., 25 Jan 2024) |
| Axial NSI ε{Aq}_{eτ}, ε{Aq}_{ττ} | World-leading bounds (∼<0.3) | (Abbaslu et al., 2 Sep 2025) |
| Sterile neutrino (Δm²₄₁ < 5 eV²) | LSND/MiniBooNE regions excluded (90% CLₛ) | (Bay et al., 2020) |
7. Continuing Developments and Future Experimentation
The MINOS+ program, via high-statistics medium-energy beam operations, refines precision oscillation parameter extraction, enables day-scale neutrino velocity measurement accuracy, and opens extended sensitivity for sterile and NSI scenarios. The methodologies and null exclusion contours from MINOS/MINOS+ inform the experimental strategy and interpretative frameworks for long-baseline projects worldwide. Anticipated theoretical and experimental advances, particularly in probing axial NSI and exotic decay modes, will further elucidate the neutrino sector’s structure as new datasets emerge in DUNE, Hyper-Kamiokande, and complementary experiments.