Almost all of the experimental data favors a normal mass ordering for neutrinos over an inverted mass ordering, but given the limitations of current experiments, the preference is almost always a weak one.
The Particle Data Group value for delta m(32) squared in normal ordering is as follows:
Taking the square root, the PDG value is a gap of 49.5 meV.
A new paper's results are consistent with the world average. The paper, its abstract, and the chart below from its supplementary materials are as follows:
This Letter reports measurements of muon-neutrino disappearance and electron-neutrino appearance and the corresponding antineutrino processes between the two NOvA detectors in the NuMI neutrino beam. These measurements use a dataset with double the neutrino mode beam exposure that was previously analyzed, along with improved simulation and analysis techniques.
A joint fit to these samples in the three-flavor paradigm results in the most precise single-experiment constraint on the atmospheric neutrino mass-splitting, Δm^2(32) = 2.431 +0.036 −0.034 (−2.479 +0.036 −0.036) × 10^−3 ~eV^2 if the mass ordering is Normal (Inverted). In both orderings, a region close to maximal mixing with sin^2(θ23) = 0.55 +0.06 −0.02 is preferred.
The NOvA data show a mild preference for the Normal mass ordering with a Bayes factor of 2.4 (corresponding to 70% of the posterior probability), indicating that the Normal ordering is 2.4 times more probable than the Inverted ordering. When incorporating a 2D Δm^2(32) --sin^2(2*θ13) constraint based on Daya Bay data, this preference strengthens to a Bayes factor of 6.6 (87%).
NOvA Collaboration, "Precision measurement of neutrino oscillation parameters with 10 years of data from the NOvA experiment" arXiv:2509.04361 (September 4, 2025).
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