Results

Results, release by release

The most recent full release in detail: best-fit values and allowed ranges for the six oscillation parameters, in both mass orderings, with the paper and its figures beside them. Every earlier release is traced parameter by parameter on the parameter history.

Conventions used throughout this site

The two squared mass gaps are δm² = m₂² − m₁² > 0 and Δm² = m₃² − ½(m₁² + m₂²), with α = sign(Δm²) distinguishing normal ordering (NO, α = +1) from inverted ordering (IO, α = −1).

Other groups quote Δm²₃₁ or Δm²₂₃ instead: those numbers are not comparable with ours at a glance. Wherever this site compares analyses, it states the conversion it applied.

March 2025 — Entering the era of subpercent precision

Updated global analysis of the known and unknown parameters of the standard three-neutrino framework, using data available at the beginning of 2025: solar, KamLAND, atmospheric, short-baseline reactor and long-baseline accelerator data.

F. Capozzi, W. Giarè, E. Lisi, A. Marrone, A. Melchiorri, A. Palazzo. Received 12 March 2025; accepted 21 April 2025; published 19 May 2025.

both orderings 1σ · 2σ · 3σ ranges NO favoured at 2.2σ Δχ²(IO−NO) = +5.0
Table I of Phys. Rev. D 111, 093006 (2025): best-fit values and allowed ranges at N σ = 1, 2, 3, for either NO or IO. The last column is the formal “1σ parameter accuracy”, defined as 1/6 of the 3σ range divided by the best-fit value, in percent. δ/π is cyclic (mod 2). Values are transcribed from the published table; nothing on this page is estimated or rounded further.
ParameterOrderingBest fit1σ range2σ range3σ range“1σ” (%)
δm² / 10⁻⁵ eV²NO, IO7.377.21 – 7.527.06 – 7.716.93 – 7.932.3
sin²θ₁₂ / 10⁻¹NO, IO3.032.91 – 3.172.77 – 3.312.64 – 3.454.5
|Δm²| / 10⁻³ eV²NO2.4952.475 – 2.5152.454 – 2.5362.433 – 2.5580.8
IO2.4652.444 – 2.4852.423 – 2.5062.403 – 2.5270.8
sin²θ₁₃ / 10⁻²NO2.232.17 – 2.272.11 – 2.332.06 – 2.382.4
IO2.232.19 – 2.302.14 – 2.352.08 – 2.412.4
sin²θ₂₃ / 10⁻¹NO4.734.60 – 4.964.47 – 5.684.37 – 5.815.1
IO5.455.28 – 5.604.58 – 5.734.43 – 5.834.3
δ/πNO1.201.07 – 1.370.88 – 1.810.73 – 2.0318
IO1.481.36 – 1.611.24 – 1.721.12 – 1.838

Δχ² projections, all data included

Fig. 3 of the paper · NO in blue, IO in red

Six panels
showing Nσ as a function of δm², |Δm²|, δ/π, sin²θ₁₂, sin²θ₁₃ and sin²θ₂₃, for
normal and inverted ordering, with all oscillation data included.

Figure 3 from F. Capozzi, W. Giarè, E. Lisi, A. Marrone, A. Melchiorri and A. Palazzo, Neutrino masses and mixing: Entering the era of subpercent precision, Phys. Rev. D 111, 093006 (2025), doi:10.1103/PhysRevD.111.093006. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license; reproduced here under those terms.

Where θ₂₃ and θ₁₃ meet

Fig. 4 of the paper · increasingly rich datasets

Regions allowed in the
sin²θ₂₃–sin²θ₁₃ plane for increasingly rich datasets, in normal ordering (top)
and inverted ordering (bottom).

Figure 4 from the same paper, same citation and licence as above.

The same table, seen at a glance

best fit · 1σ · 3σ · each row on its own scale

δm² / 10⁻⁵ eV² 3σ: 6.93 – 7.93 1σ: 7.21 – 7.52 best fit 7.37 7.37 |Δm²| / 10⁻³ eV² (NO) 3σ: 2.433 – 2.558 1σ: 2.475 – 2.515 best fit 2.495 2.495 |Δm²| / 10⁻³ eV² (IO) 3σ: 2.403 – 2.527 1σ: 2.444 – 2.485 best fit 2.465 2.465 sin²θ₁₂ / 10⁻¹ 3σ: 2.64 – 3.45 1σ: 2.91 – 3.17 best fit 3.03 3.03 sin²θ₁₃ / 10⁻² (NO) 3σ: 2.06 – 2.38 1σ: 2.17 – 2.27 best fit 2.23 2.23 sin²θ₁₃ / 10⁻² (IO) 3σ: 2.08 – 2.41 1σ: 2.19 – 2.3 best fit 2.23 2.23 sin²θ₂₃ / 10⁻¹ (NO) 3σ: 4.37 – 5.81 1σ: 4.6 – 4.96 best fit 4.73 4.73 sin²θ₂₃ / 10⁻¹ (IO) 3σ: 4.43 – 5.83 1σ: 5.28 – 5.6 best fit 5.45 5.45 δ/π (NO) 3σ: 0.73 – 2.03 1σ: 1.07 – 1.37 best fit 1.2 1.2 δ/π (IO) 3σ: 1.12 – 1.83 1σ: 1.36 – 1.61 best fit 1.48 1.48

Every row is drawn on its own axis, so the widths compare precision rather than magnitude. Values are those of Table I above; the figure is generated from them by tools/make_figures.py, not drawn by hand.

What changed

|Δm²| is now constrained at the 0.8% level — the first oscillation parameter to enter the subpercent precision era — against 1.1% in the previous update; the paper underlines in the same breath that there are issues about systematics which might affect that error estimate. The uncertainty on sin²θ₁₃ falls to 2.4%, from about 3%. For sin²θ₂₃ the two quasi-degenerate minima are closer than before, differing by roughly 15% against about 25% previously. Constraints on δ are similar to before within large uncertainties, with a weaker rejection of CP conservation in NO. The overall offset between the orderings is now Nσ = √5.0 = 2.2, down from 2.5σ.

Not included

The first published SNO+ reactor results are not included: they constrain δm² with an error larger than the one above by a factor of about 6, and only under a prior on θ₁₂. SNO+ is nevertheless expected to surpass the present δm² accuracy on (δm², θ₁₂) within a few years.

Since this release: the (1, 2) sector, updated

A partial update revises two of the six parameters above. Phys. Rev. D 114, 016026 (2026) (arXiv:2511.21650) adds the first JUNO results and the latest SNO+ data to the 2025 analysis and gives δm² = 7.48 (1σ 7.39 – 7.58) in units of 10⁻⁵ eV² and sin²θ₁₂ = 0.3085 (1σ 0.3010 – 0.3156). It quotes no new values for |Δm²|, sin²θ₁₃, sin²θ₂₃ or δ, which stand as in the table above. Both releases are on the parameter history, with the table each number was transcribed from.

Machine-readable data

planned for this release

Δχ² profiles and the tables above will be published here as documented files at stable URLs — the kind of thing you can fetch from a script and cite — under data/<release>/. They are exported from the analysis by a dedicated step; the analysis code itself stays where it belongs and is never part of this site.

Nothing is linked from this section yet: the export runs when the release material is prepared, and a link that does not resolve is worse than no link. What does exist today is the parameter register — every value on this site, with its source — published as JSON and CSV on the parameter history page.