Neutrino oscillation parameters
Bari Group 2026.a Preliminary

Key numbers

The questions the data are asked most often, answered for each data set. Every number is read from the 1D profiles, on the common scale of the two orderings (Δχ² from the overall best fit), with one degree of freedom: Nσ = √Δχ².

Synopsis figures

One panel per parameter, Nσ = √(Δχ²) against the parameter, both orderings on the joint scale.

Two-dimensional planes

The five planes of the Δχ² surfaces, one figure per plane, both mass orderings overlaid. Produced by the notebook from the tables above. The one-dimensional profiles are the synopsis figures just above.

Data files

Preliminary The Δχ² tables (1D, 2D and the full 6D χ²), the tables as PDF, the notebook and the release package will be published with the paper. Until then the values on this site are preliminary and may change.

The three data sets

Named by the baseline of the reactor sector rather than by experiment, because that is what the physics depends on. The tags below are the ones the figures carry; every experiment is listed once, here.

How to read the tables

One point deserves attention before any use of these files.

offset = J_IO − J_NO          (positive → NO favoured)

Dchi2_joint_NO = Dchi2_NO + max(0, −offset)
Dchi2_joint_IO = Dchi2_IO + max(0, +offset)

Conventions

Nσ = √(Δχ²) with one degree of freedom, as in our papers. The six parameters live on different grids, so the tables are in long format: one row per node, columns parameter value unit Dchi2_NO Dchi2_IO. All three data sets give exact profiles, in 1D and in 2D: at every node all the other parameters and all the nuisances are minimised over — each file states it in its header.

Notation, and how to translate it

Different global analyses use different mass-squared variables. Getting the translation wrong is the single easiest way to misread a comparison, so we state ours explicitly.

What we use

δm² = m₂² − m₁²                                   (positive by definition)

Δm² = m₃² − (m₁² + m₂²)/2  =  (Δm²₃₁ + Δm²₃₂)/2      ( > 0 in NO,  < 0 in IO )

Δm² is the semisum of the two atmospheric splittings, and we quote it with its sign: positive in the normal ordering, negative in the inverted one. Every IO row below therefore carries a negative Δm². A bare magnitude would not say which ordering a number belongs to, and the two best fits are different numbers with different precisions, so wherever a single value appears on this page the ordering is named beside it. Our LaTeX tables carry the same sign. Where a symbol appears between bars it is a magnitude on purpose: that is what the comparison with NuFIT and Valencia needs, since those groups quote |Δm²₃₂| and |Δm²₃₁|.

Translating to Δm²₃₁ and Δm²₃₂

Δm²₃₁ = Δm² + δm²/2        Δm²₃₂ = Δm² − δm²/2        (both orderings)

IO, on magnitudes:   |Δm²₃₂| = |Δm²| + δm²/2       |Δm²₃₁| = |Δm²| − δm²/2

These are exact identities. They follow from Δm²₃₁ = Δm²₃₂ + δm², which is the definition of δm² rearranged: the semisum then gives Δm² = Δm²₃₁ − δm²/2 = Δm²₃₂ + δm²/2. Because Δm² carries its sign, the first line holds in both orderings. In the inverted one Δm² and both Δm²₃_ℓ are negative, so taking magnitudes exchanges the two roles and the plus sign passes to the «32».

NuFIT quotes Δm²₃₁ for NO and Δm²₃₂ for IO; the Valencia fit quotes |Δm²₃₁| for both. The comparison table below is labelled accordingly.

Propagating the error

For y = |Δm²| + δm²/2 — that is Δm²₃₁ in NO and |Δm²₃₂| in IO — the full Gaussian formula is var(y) = var(Δm²) + var(δm²)/4 + cov(Δm², δm²). The variances are those of the tables above; the correlation ρ is measured, not assumed zero. It turns out small, and the last column shows how little it matters — but that is a result, not an assumption.

Our results — final combination (with JUNO + atmospheric)

The relative uncertainty uses the symmetrised 1σ error, (σ₊+σ₋)/2. ⊕ separates disjoint allowed intervals.

Comparison with other global analyses

Upper line: best fit with 1σ errors. Lower line, in grey: the 3σ range.

What’s new, and how to cite

New data in release 2026.a, with respect to our previous analysis:

How to cite

Please cite the paper that accompanies this release; its reference will appear here. To point to these tables themselves, cite the release with its version:

@misc{BariGroup2026a,
  author       = {{Bari Group}},
  title        = {Global analysis of neutrino oscillation data, release 2026.a},
  year         = {2026},
  note         = {Preliminary version of 2026-10-15},
  howpublished = {\url{https://global-nu.org/results.html}}
}

Questions, problems with a file, requests: antonio.marrone@ba.infn.it.