One of the major outstanding questions in neutrino physics is whether the neutrino masses have a "normal hierarchy", or an "inverted hierarchy." We are close to having an answer to that question.

The sum of the neutrino masses in an inverted hierarchy, we know from neutrino oscillation data, cannot be less than 98.6 meV. In a normal hierarchy, the sum of the neutrino masses must be at least a bit more than 65.34 meV. A global look at various kinds of astronomy data suggests that there is a 95% chance that the sum of the three neutrino masses is, in fact, 90 meV or less. This strongly favors a "normal hierarchy" of neutrino masses.

The state of the art measurements of the difference between the first and second neutrino mass eigenstate is roughly 8.66 +/- 0.12 meV, and the difference between the second and third neutrino mass eigenstate is roughly 49.5 +/- 0.5 meV, which implies that the sum of the three neutrino mass eigenstates cannot be less than about 65.34 meV with 95% confidence.

So, this also gives us absolute neutrino mass estimates that have relative precision comparable to that of the experimental value of lighter quark masses and precision in absolute terms that is truly remarkable. It narrows the range of each of the neutrino masses to a nearly perfectly correlated window only a bit larger than +/- 4 meV. This is a roughly 33% improvement over the previous state of the art precision with which the absolute neutrino masses can be estimated.

The bottom line is that the range of the three neutrino masses that would be consistent with experimental data is approximately as follows (with the location of each mass within the range being highly correlated with the other two and the sum):

Mv1 0-7.6 meV

Mv2 8.42-16.1 meV

Mv3 56.92-66.2 meV

Sum of all three neutrino masses should be in the range: 65.34-90 meV

Realistically, I think that most people familiar with the question would subjectively favor results at the low end of these ranges, not least because the best fit value for the sum of the three neutrino masses based on astronomy data is significantly lower than the 95% confidence interval upper bound on the sum of the three neutrino masses.

The bottom line is that the range of the three neutrino masses that would be consistent with experimental data is approximately as follows (with the location of each mass within the range being highly correlated with the other two and the sum):

Mv1 0-7.6 meV

Mv2 8.42-16.1 meV

Mv3 56.92-66.2 meV

Sum of all three neutrino masses should be in the range: 65.34-90 meV

Realistically, I think that most people familiar with the question would subjectively favor results at the low end of these ranges, not least because the best fit value for the sum of the three neutrino masses based on astronomy data is significantly lower than the 95% confidence interval upper bound on the sum of the three neutrino masses.

In a Majorana neutrino mass type model, the neutrino mass is very tightly related to the rate of neutrinoless double beta decay that occurs, something that has not yet been observed with credible experimental data. The narrow window for the absolute neutrino masses also results in a narrow window for the expected rate of neutrinoless double beta decay that is not terribly far from the current experimental upper bound on the rate of that phenomena from neutrinoless double beta decay experiments. So, we may be very close to proving or disproving the Majorana v. Dirac neutrino mass question.

If neutrinos do have a "normal hierarchy", as every other class of Standard Model fermions does, this also suggests that whatever mechanism gives rise to the relative fermion masses in the Standard Model (including the neutrinos) inherently leads to a normal hierarchy, rather than being arbitrary.

If neutrinos do have a "normal hierarchy", as every other class of Standard Model fermions does, this also suggests that whatever mechanism gives rise to the relative fermion masses in the Standard Model (including the neutrinos) inherently leads to a normal hierarchy, rather than being arbitrary.

The paper and its abstract are as follows:

Sunny Vagnozzi, et al., "Unveiling ν secrets with cosmological data: neutrino masses and mass hierarchy" (January 27, 2017).Using some of the latest cosmological datasets publicly available, we derive the strongest bounds in the literature on the sum of the three active neutrino masses, Mν. In the most conservative scheme, combining Planck cosmic microwave background (CMB) temperature anisotropies and baryon acoustic oscillations (BAO) data, as well as the up-to-date constraint on the optical depth to reionization (τ), the tightest 95% confidence level (C.L.) upper bound we find is Mν<0.151~eV. The addition of Planck high-ℓ polarization tightens the bound to Mν<0.118~eV.Further improvements are possible when a less conservative prior on the Hubble parameter is added, bringing down the 95%~C.L. upper limit to ∼0.09~eV. The three aforementioned combinations exclude values of Mν larger than the minimal value allowed in the inverted hierarchical (IH) mass ordering, 0.0986~eV, at ∼82%~C.L., ∼91%~C.L., and ∼96%~C.L. respectively.A proper model comparison treatment shows that the same combinations exclude the IH at ∼64%~C.L., ∼71%~C.L., and ∼77%~C.L. respectively. We test the stability of the bounds against the distribution of the total mass Mν among the three mass eigenstates, finding that these are relatively stable against the choice of distributing the total mass among three (the usual approximation) or one mass eigenstate. Finally, we compare the constraining power of measurements of the full-shape galaxy power spectrum versus the BAO signature, from the BOSS survey. Even though the latest BOSS full shape measurements cover a larger volume and benefit from smaller error bars compared to previous similar measurements, the analysis method commonly adopted results in their constraining power still being less powerful than that of the extracted BAO signal. (abridged)