Analysis results — Antonio Marrone

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Latest · October 2026

Bari Release 2026.a, after the second JUNO data release Preliminary

A full release of the global analysis: long-baseline accelerator, solar, reactor and atmospheric data, with the second JUNO data release. Normal ordering is now favoured at 3.9σ, and the precision on all three of δm², sin²θ₁₂ and |Δm²| improves.

Preliminary The paper is in preparation: these values may still change, and the Δχ² tables, the notebook and the data files will be published with it.

Full results on global-nu.org

Mass ordering

Normal, 3.9σ

Δχ²_IO−NO = 15.34, final combination (2.2σ in March 2025)

Solar splitting

7.465 ×10⁻⁵ eV²

δm² · 1σ accuracy 1.0 %

Atmospheric splitting

2.472 ×10⁻³ eV²

|Δm²| · 1σ accuracy 0.6 %, the tightest of the six

Final combination, LBL Acc + Solar + Reac + Atmos (with JUNO): best fits and allowed ranges at N σ = 1, 2, 3 for either mass ordering, each referred to its own minimum, one degree of freedom. Each parameter is profiled, i.e. minimised over the other five and over all nuisances. The last column is the 1σ accuracy, in percent: one sixth of the 3σ range divided by the best fit, for every parameter — the definition global-nu.org uses for this release. δm² = m₂² − m₁², Δm² = m₃² − (m₁² + m₂²)/2 (negative in IO; its modulus is given). Preliminary values, version of 15 October 2026.
Parameter	Ordering	Best fit	1σ range	2σ range	3σ range	“1σ” (%)
δm² / 10⁻⁵ eV²	NO	7.465	7.386 – 7.538	7.312 – 7.609	7.239 – 7.681	1.0
δm² / 10⁻⁵ eV²	IO	7.439	7.364 – 7.516	7.292 – 7.589	7.218 – 7.662	1.0
sin²θ₁₂	NO	0.3047	0.2993 – 0.3104	0.2940 – 0.3160	0.2888 – 0.3217	1.8
sin²θ₁₂	IO	0.3036	0.2981 – 0.3092	0.2928 – 0.3150	0.2876 – 0.3208	1.8
\|Δm²\| / 10⁻³ eV²	NO	2.4720	2.4586 – 2.4853	2.4454 – 2.5007	2.4317 – 2.5174	0.6
\|Δm²\| / 10⁻³ eV²	IO	2.4810	2.4648 – 2.4965	2.4487 – 2.5134	2.4291 – 2.5293	0.7
sin²θ₁₃	NO	0.0222	0.0216 – 0.0227	0.0211 – 0.0233	0.0205 – 0.0238	2.5
sin²θ₁₃	IO	0.0223	0.0217 – 0.0228	0.0212 – 0.0234	0.0206 – 0.0239	2.5
sin²θ₂₃	NO	0.4908	0.4703 – 0.5383	0.4557 – 0.5594	0.4439 – 0.5735	4.4
sin²θ₂₃	IO	0.5446	0.5188 – 0.5592	0.4546 – 0.5716	0.4408 – 0.5819	4.3
δ / π	NO	1.19	1.05 – 1.34	0.92 – 1.65	0.79 – 1.95	16.3
δ / π	IO	1.52	1.40 – 1.63	1.28 – 1.74	1.16 – 1.84	7.5

The questions asked most often, for the final combination and for the same data without the atmospheric ones. Every number is read from the one-dimensional profiles on the common scale of the two orderings (Δχ² from the overall best fit), with N σ = √Δχ². Reac: all reactor baselines, JUNO included; Atmos: Super-Kamiokande, IceCube/DeepCore and KM3NeT/ORCA6.
Data set	Mass ordering	θ₂₃ octant	sin²θ₂₃ = 1/2	CP conservation
LBL Acc + Solar + Reac + Atmos	NO at 3.9σ (Δχ² = 15.34)	first; other at 0.3σ	0.3σ	δ = 0 at 3.2σ, δ = π at 1.4σ
LBL Acc + Solar + Reac	NO at 2.0σ (Δχ² = 3.99)	first; other at 0.5σ	0.5σ	δ = 0 at 2.7σ, δ = π at 1.2σ

Six panels, one per oscillation parameter: N sigma against the parameter for the final combination, normal ordering in blue, inverted ordering in red; inverted ordering sits about four sigma above normal. — Preliminary Final combination (LBL Acc + Solar + Reac + Atmos): N σ = √Δχ² for each parameter, both orderings on the common scale (solid), and inverted ordering referred to its own minimum (dashed). The other data sets and the two-dimensional planes are on global-nu.org.

Found an error in these results or on this page? Please write to antonio.marrone@uniba.it or antonio.marrone@ba.infn.it.

Update · November 2025

The (1, 2) parameters after the first JUNO results

A partial update of the March 2025 release: the first JUNO results and the latest SNO+ data, added as external constraints. They revise δm² and sin²θ₁₂ alone — |Δm²|, sin²θ₁₃, sin²θ₂₃ and δ stand as in the release below, which the paper finds “not perceptibly changed”.

arXiv:2511.21650 Phys. Rev. D 114, 016026

F. Capozzi, E. Lisi, F. Marcone, A. Marrone, A. Palazzo.

Solar splitting

7.48 ± 0.10 ×10⁻⁵ eV²

δm² · 1σ accuracy 1.3 % (was 2.3 %)

Solar mixing angle

0.3085 ± 0.0073

sin²θ₁₂ · 1σ accuracy 2.4 % (was 4.5 %)

Correlation

ρ = −0.20

between the two errors, Eq. (1) of the paper

Table I of Phys. Rev. D 114, 016026 (2026): best-fit values and allowed ranges at N σ = 1, 2, 3, for the 2024 analysis and for this work with SNO+ alone and with SNO+ and JUNO. The last column is the formal “1σ parameter accuracy” defined there — one sixth of the ±3σ range, divided by the best fit, in percent. δm² = m₂² − m₁². Table I assumes equiprobable orderings (Δχ²_IO−NO = 0); Fig. 1 of the paper shows both orderings, with the offset Δχ²_IO−NO = 5.0 of the March 2025 release, and the paper finds no appreciable difference between the two orderings for these two parameters.
Analysis	Parameter	Best fit	1σ range	2σ range	3σ range	“1σ” (%)
All data 2024	δm² / 10⁻⁵ eV²	7.37	7.21 – 7.52	7.06 – 7.71	6.93 – 7.93	2.3
All data 2024	sin²θ₁₂ / 10⁻¹	3.03	2.91 – 3.17	2.77 – 3.31	2.64 – 3.45	4.5
w/ SNO+ 2025	δm² / 10⁻⁵ eV²	7.44	7.30 – 7.61	7.17 – 7.80	7.04 – 7.99	2.1
w/ SNO+ 2025	sin²θ₁₂ / 10⁻¹	3.06	2.93 – 3.19	2.80 – 3.33	2.67 – 3.47	4.4
w/ SNO+ & JUNO 2025	δm² / 10⁻⁵ eV²	7.48	7.39 – 7.58	7.30 – 7.68	7.21 – 7.78	1.3
w/ SNO+ & JUNO 2025	sin²θ₁₂ / 10⁻¹	3.085	3.010 – 3.156	2.939 – 3.230	2.866 – 3.303	2.4

Written as correlated 1σ errors, Eq. (1) of the paper reads

δm² / 10⁻⁵ eV² = 7.48 ± 0.10, sin²θ₁₂ / 10⁻¹ = 3.085 ± 0.073, ρ = −0.20,

for all oscillation constraints available as of 2025. The errors are, to a very good approximation, symmetric and linear in the number of standard deviations — which is why the 2σ and 3σ ranges above are so close to simple multiples of the 1σ one, and a departure from that pattern in a future release would itself be news.

The update is dominated by JUNO. The paper's own intermediate row, with SNO+ added but not JUNO, still gives δm² = 7.44 at 2.1 %: it is JUNO that takes the accuracy on δm² from 2.1 % to 1.3 %, while the remaining data shift the best fit slightly and reduce JUNO's own errors by a factor of about 0.84.

How far the fourth digit means anything. The paper is explicit that subleading effects it does not zero out can move the best fits at the level of a few parts per thousand — the fourth significant figure of sin²θ₁₂, sometimes the third once the fourth is rounded. Four digits are quoted so that the 1σ error can carry two, not because the last one is determined.

Release · March 2025

Entering the era of subpercent precision

Global three-flavour analysis including the latest solar, atmospheric, reactor and long-baseline accelerator data, combined with cosmological constraints.

arXiv:2503.07752 Phys. Rev. D 111, 093006

F. Capozzi, W. Giarè, E. Lisi, A. Marrone, A. Melchiorri, A. Palazzo.

Best-fit values and 3σ ranges from the 2025 global analysis (Table I of the paper), normal ordering. The fractional accuracy is the 1σ precision defined there as one sixth of the 3σ range, divided by the best fit. Δm² is defined as m₃² − (m₁² + m₂²)/2. See the paper for the inverted ordering. NO is favoured over IO at 2.2σ.
Parameter	Best fit	3σ range	1σ precision
δm² / 10⁻⁵ eV²	7.37	6.93 – 7.93	2.3 %
sin²θ₁₂	0.303	0.264 – 0.345	4.5 %
\|Δm²\| / 10⁻³ eV²	2.495	2.433 – 2.558	0.8 %
sin²θ₁₃	0.0223	0.0206 – 0.0238	2.4 %
sin²θ₂₃	0.473	0.437 – 0.581	5.1 %
δ / π	1.20	0.73 – 2.03	18 %

χ² profiles, two-dimensional allowed regions and the machine-readable tables for this release are available from the authors on request. Both orderings, the 1σ and 2σ ranges and the comparison with other groups are on global-nu.org.

Data

Machine-readable data

None of the published releases on this page came with a public machine-readable dataset, and none will be rebuilt after the fact. For the March 2025 release, χ² profiles and tables are available from the authors on request. For the preliminary Release 2026.a, the Δχ² tables and data files will be published with its paper; until then they are available to authorised readers only, below. Public Δχ² profiles and tables, as documented files at stable URLs, are planned on global-nu.org for future releases. What is public today is the parameter register — every value quoted there, with its source — as JSON and CSV on the parameter history page.

Restricted · JUNO 2026

Bari group results — second release

Δχ² tables, one- and two-dimensional profiles and the figures of the Bari global analysis including the JUNO second release, served as an interactive notebook that runs entirely in the browser. The underlying .npz and text tables are downloadable from the same page.

Access is restricted until the paper is out; the preliminary values are public, above. Credentials on request.

Open the results →

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Earlier releases

Unfinished fabric of the three neutrino paradigm
F. Capozzi, E. Di Valentino, E. Lisi, A. Marrone, A. Melchiorri, A. Palazzo

Phys. Rev. D 104, 083031 (2021) arXiv:2107.00532
Global constraints on absolute neutrino masses and their ordering — Addendum
F. Capozzi, E. Di Valentino, E. Lisi, A. Marrone, A. Melchiorri, A. Palazzo

Phys. Rev. D 101, 116013 (2020)
Current unknowns in the three neutrino framework
F. Capozzi, E. Lisi, A. Marrone, A. Palazzo

Prog. Part. Nucl. Phys. 102, 48 (2018) arXiv:1804.09678

Complete publication list →