Release March 2025 · PRD 111, 093006

Global analyses of neutrino
oscillation data

The Bari global analysis of neutrino oscillation data, published openly: best fits, allowed ranges, both mass orderings, and a parameter register you can download as JSON or CSV.

The six parameters, as measured

δm² / 10⁻⁵ eV² 3σ: 6.93 – 7.93 1σ: 7.21 – 7.52 best fit 7.37 7.37 |Δm²| / 10⁻³ eV² 3σ: 2.433 – 2.558 1σ: 2.475 – 2.515 best fit 2.495 2.495 sin²θ₁₂ / 10⁻¹ 3σ: 2.64 – 3.45 1σ: 2.91 – 3.17 best fit 3.03 3.03 sin²θ₁₃ / 10⁻² 3σ: 2.06 – 2.38 1σ: 2.17 – 2.27 best fit 2.23 2.23 sin²θ₂₃ / 10⁻¹ 3σ: 4.37 – 5.81 1σ: 4.6 – 4.96 best fit 4.73 4.73 δ/π 3σ: 0.73 – 2.03 1σ: 1.07 – 1.37 best fit 1.2 1.2 arXiv:2503.07752

Best fit with 1σ and 3σ ranges, normal ordering, from Table I of Phys. Rev. D 111, 093006 (2025). Full tables and both orderings are on the results page.

Best fits

normal ordering · arXiv:2503.07752, (1,2) sector updated in arXiv:2511.21650

Full tables and ranges →
sin²θ₁₂0.3085formal 1σ accuracy 2.4% · 20262006 → 2026
sin²θ₁₃0.0223formal 1σ accuracy 2.4%2006 → 2025
sin²θ₂₃0.473formal 1σ accuracy 5.1%2006 → 2025
δm² / 10⁻⁵ eV²7.48m₂² − m₁² > 0 · 20262006 → 2026
|Δm²| / 10⁻³ eV²2.495m₃² − (m₁²+m₂²)/22006 → 2025
δ/π1.20CP phase, cyclic mod 22012 → 2025

Normal ordering is favoured at 2.2σ; the χ² offset between the orderings is Δχ²(IO−NO) = +5.0. Four of the six values above — sin²θ₁₃, sin²θ₂₃, |Δm²| and δ/π, together with that ordering preference — are from Table I of Phys. Rev. D 111, 093006 (2025), the most recent full release, in the conventions stated there.

The two marked 2026 — δm² and sin²θ₁₂ — are newer. They come from Table I of Phys. Rev. D 114, 016026 (2026) (arXiv:2511.21650), which adds the first JUNO results and the latest SNO+ data to the 2025 analysis. It revises the (1,2) sector alone and does not touch the other four parameters, so this card set is the newest published value for each — not a single fit. Both papers define the percentage the same way, as their own “formal 1σ parameter accuracy”: a sixth of the 3σ range divided by the best fit, which is not the ordinary 1σ fractional uncertainty and does not equal half the 1σ range over the best fit. The parameter history carries every release, value by value.

How the precision improved

formal 1σ accuracy · logarithmic scale

1% 2% 5% 10% 20% 2011 2012 2013 2016 2017 2018 2021 2025 2026 δm², 2011: 1σ accuracy 2.6% δm², 2012: 1σ accuracy 2.6% δm², 2013: 1σ accuracy 2.6% δm², 2016: 1σ accuracy 2.4% δm², 2017: 1σ accuracy 2.3% δm², 2018: 1σ accuracy 2.2% δm², 2021: 1σ accuracy 2.3% δm², 2025: 1σ accuracy 2.3% δm², 2026: 1σ accuracy 1.3% |Δm²|, 2011: 1σ accuracy 4.3% |Δm²|, 2012: 1σ accuracy 2.9% |Δm²|, 2013: 1σ accuracy 2.6% |Δm²|, 2016: 1σ accuracy 1.7% |Δm²|, 2017: 1σ accuracy 1.6% |Δm²|, 2018: 1σ accuracy 1.4% |Δm²|, 2021: 1σ accuracy 1.1% |Δm²|, 2025: 1σ accuracy 0.84% sin²θ₁₂, 2011: 1σ accuracy 5.4% sin²θ₁₂, 2012: 1σ accuracy 5.4% sin²θ₁₂, 2013: 1σ accuracy 5.4% sin²θ₁₂, 2016: 1σ accuracy 5.8% sin²θ₁₂, 2017: 1σ accuracy 5.8% sin²θ₁₂, 2018: 1σ accuracy 4.4% sin²θ₁₂, 2021: 1σ accuracy 4.5% sin²θ₁₂, 2025: 1σ accuracy 4.5% sin²θ₁₂, 2026: 1σ accuracy 2.4% sin²θ₁₃, 2011: 1σ accuracy 34% sin²θ₁₃, 2012: 1σ accuracy 10% sin²θ₁₃, 2013: 1σ accuracy 8.5% sin²θ₁₃, 2016: 1σ accuracy 4.8% sin²θ₁₃, 2017: 1σ accuracy 3.9% sin²θ₁₃, 2018: 1σ accuracy 3.8% sin²θ₁₃, 2021: 1σ accuracy 3% sin²θ₁₃, 2025: 1σ accuracy 2.4% sin²θ₂₃, 2011: 1σ accuracy 12% sin²θ₂₃, 2012: 1σ accuracy 13% sin²θ₂₃, 2013: 1σ accuracy 9.6% sin²θ₂₃, 2016: 1σ accuracy 9% sin²θ₂₃, 2017: 1σ accuracy 9.2% sin²θ₂₃, 2018: 1σ accuracy 5.2% sin²θ₂₃, 2021: 1σ accuracy 6.7% sin²θ₂₃, 2025: 1σ accuracy 5.1% δ/π, 2018: 1σ accuracy 15% δ/π, 2021: 1σ accuracy 16% δ/π, 2025: 1σ accuracy 18% δ/π sin²θ₂₃ sin²θ₁₃ sin²θ₁₂ δm² |Δm²|

Each line is one parameter’s formal 1σ accuracy — a sixth of its 3σ range over its best fit — as published in each release. Computed from the same tables the parameter history is built on.