Background
Data from W and Z boson decays and from cosmology measurements, strongly favor a model with exactly three active neutrino flavors, as do requirements for mathematical consistent in the Standard Model of Particle Physics, which requires that each generation of Standard Model fermions (i.e. an up-like quark, a down-like quark, an electron-like charged lepton, and a neutrino) must be complete with four members. The lower bound on a fourth active neutrino mass is on the order of 45,000,000,000,000 meV, while we know that none of the other three active neutrino masses are more than about 900 meV, and we have strong indications that the largest of the three active neutrino masses is no more than about 70 meV.
When the Standard Model was first formulated in the 1970s, neutrinos were assumed to be massless fermions. Experiments proved that this couldn't be the case in 1998, and that neutrinos change flavors and oscillate between their three mass eigenstates. Since then, scientists have worked to determine their mass and additional properties arising from the fact that they have mass, which has culminated in a basic three favor, Dirac neutrino model of neutrino oscillation to which the data has been fit.
This neutrino oscillation behavior is characterized by two mass differences Δm(21) and Δm(32), whether the masses are in a "normal" or "inverted" hierarchy, and four parameters of the PMNS matrix: three of which describe the probability of each of the possible transitions between the three neutrino flavors, and one of which δCP describes charge parity violation (i.e. how those transition probabilities differ between neutrinos and antineutrinos).
The two mass differences have been measured to decent precision. A normal mass hierarchy is favored by the experimental data, but not to terribly great statistical significance (the preference is close to two sigma). The three main mixing angles of the PMNS matrix have been measured to reasonable but modest precision, although it isn't entirely established if one of them is a bit less than 45º or a bit more than 45º (the data increasing favors a value that is a bit more than 45º). Attempts to measure δCP are very imprecise and generally can't entirely rule out the possibility that there is no CP violation in neutrino oscillation, the best fit values of measurements of δCP consistently favor near maximum CP violation in neutrino oscillations.
The world average measured value of those parameters are as follows (according to the Particle Data Group):
In addition, to fully characterize the properties of neutrinos in the basic three flavor, Dirac neutrino model to which experimental data is fitted, one needs to know the absolute rest mass of at least one of the neutrino mass eigenstates. The experimental upper bound on the mass of the lightest absolute neutrino mass eigenstate is about 800 meV. The experimental lower bound on the sum of the three neutrino mass eigenstates is on the order of 58 meV for a "normal" hierarchy of neutrino masses, and 110 meV. for an "inverted" hierarchy of neutrino masses Reasonably robust upper bounds on the sum of the three neutrino masses from cosmology models and astronomy measurements favor an upper bound for the sum of the three neutrino masses to around 130 meV, with some measurements putting it below the 110 meV cap allowed for an inverted hierarchy for neutrino masses with some more aggressive theoretical assumptions.
The New Paper
A new paper combines the latest data from two major neutrino physics collaborations (NOvA and T2K) to tighten up the precision of measurements of the Δm(32) and δCP parameters of neutrino oscillations, which is hard to do with a single collaboration's data, because the observables in each experiment depend upon more than one parameter, and it is hard to tell with just a single experiment's data, which parameter is driving those observables. But, since the mix of parameters that drive the observables in each experiment is different (in part, by design to allow for just this kind of combined data analysis), when the two collaborations' data are combined, these degeneracies in each individual collaboration's data can be minimized.
The new paper below improves the precision of the measurement of Δm(32) a bit, and also makes for a still very imprecise, but improved, measurement of δCP.
The new combined measurement for Δm(32) is at the very low end of the current the world average plus or minus two sigma range.
The new paper rules out the possibility of zero CP violation in neutrino mixing at the 3 sigma level for an inverted neutrino mass hierarchy assumption, and at a roughly 2.4 sigma level of significance for a normal neutrino mass hierarchy assumption.
The landmark discovery that neutrinos have mass and can change type (or "flavor") as they propagate -- a process called neutrino oscillation -- has opened up a rich array of theoretical and experimental questions being actively pursued today.
Neutrino oscillation remains the most powerful experimental tool for addressing many of these questions, including whether neutrinos violate charge-parity (CP) symmetry, which has possible connections to the unexplained preponderance of matter over antimatter in the universe. Oscillation measurements also probe the mass-squared differences between the different neutrino mass states (Δm^2), whether there are two light states and a heavier one (normal ordering) or vice versa (inverted ordering), and the structure of neutrino mass and flavor mixing.
Here, we carry out the first joint analysis of data sets from NOvA and T2K, the two currently operating long-baseline neutrino oscillation experiments (hundreds of kilometers of neutrino travel distance), taking advantage of our complementary experimental designs and setting new constraints on several neutrino sector parameters.
This analysis provides new precision on the Δm(32)^2 mass difference, finding 2.43+0.04−0.03 (−2.48+0.03−0.04) × 10^−3 eV^2 in the normal (inverted) ordering, as well as a 3σ interval on δCP of [−1.38π, 0.30π] ([−0.92π, −0.04π]) in the normal (inverted) ordering. The data show no strong preference for either mass ordering, but notably if inverted ordering were assumed true within the three-flavor mixing paradigm, then our results would provide evidence of CP symmetry violation in the lepton sector.
NOvA, T2K Collaborations, "Joint neutrino oscillation analysis from the T2K and NOvA experiments" arXiv:2510.19888 (October 22, 2025).
Further Neutrino Property Issues
Additional parameters are needed if neutrinos are actually Majorana particles (i.e. if they are their own antiparticles), or if they oscillate with a "sterile" right handed neutrino which only interacts via neutrino oscillation (and not via the electromagnetic, weak, or strong forces of the Standard Model) which is often proposed as a way for Dirac neutrinos to acquire mass in what is called a see-saw mechanism.
Most physicists believe that one of these two possibilities should be possible to give rise to a mechanism for mass generation in neutrinos. Mass generation via the Higgs mechanism is not a good fit for neutrinos since all neutrinos are "left handed" in parity, and all antineutrinos are "right handed" in parity, unlike all other Standard Model fermions which have both left and right parity versions of both their particles and their antiparticles, making four states possible.
The most definitive phenomenological parameter of Majorana neutrinos would be neutrinoless double beta decay, which has not been observed to high precision. But neutrinoless double beta decays involving Majorana neutrinos is a function of their absolute mass scale. It is more rare to the extent that neutrinos are less massive. And, current bounds on neutrinoless double beta decay are not so strong that this can be ruled out for reasonable neutrino mass scales, although it's getting close to that point. Majorana neutrinos would also have a more complicated oscillation behavior involving more mixing parameters than the Dirac neutrino model.
A Dirac neutrino model with a see-saw mechanism involving oscillation with a sterile neutrino would imply that the transition probabilities of the PMNS matrix parameters wouldn't be unitary. In other words, the probabilities of all the three flavor model transitions wouldn't add up to 100%, because some small percentage of neutrino oscillations would be to one or more sterile neutrino flavors. So far, the observed PMNS matrix parameters are consistent with unitarity. But since the measured parameters each have uncertainties, there is room within those uncertainties for transitions to an additional sterile neutrino flavor (or even to multiple sterile neutrino flavors). The upper bound on missing neutrino transition probabilities is quite low, however, and to make a see-saw mechanism work with such small experimentally allowed transition probabilities, the mass of a hypothetical sterile neutrino would have to be very high.
For the record, I don't like either solution and think that we need to find a "third way" mechanism for generating neutrino mass, although I don't know what it would be.
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