In another thread a point was raised that current theory (or perhaps experimental results) establishes a definite (or appromimate) relationship between the average and the variance of the rest masses for the three flavors of neutrinos. I have tried to educated myself from material I can find on the internet, but I find myself confused by what I read. I would much appreciate any help. (The other thread is: https://www.physicsforums.com/threads/neutrinos-and-conservation-laws.820061/ ) The following is from an article, with a corresponding quote, that seem to disccuss this question, but I feel my understanding remains marginal at best. http://arxiv.org/abs/1308.5870 A consistent picture emerges and including a prior for the cluster constraints and BAOs we find that: for an active neutrino model with 3 degenerate neutrinos, ∑mν=(0.320±0.081)eV, whereas for a sterile neutrino, in addition to 3 neutrinos with a standard hierarchy and ∑mν=0.06eV, meffν,sterile=(0.450±0.124)eV and ΔNeff=0.45±0.23.I find this languge confusing. What are the conceptual differences between: 1) an active neutrino model with 3 degenerate neutrinos, ∑mν=(0.320±0.081)eV, AND 2) 3 neutrinos with a standard hierarchy and ∑mν=0.06eV, meffν,sterile=(0.450±0.124)eV and ΔNeff=0.45±0.23? I interpret (1) to mean the the sum of the rest masses for the three flavors of neutrinos is 320 meV, and the experimental error range for this sum is +/- 81 meV. I don't undestand (2) at all. Can someone offer an explanation? Assuming I am correct about (1) and ignoring the error range, I interpret that the possible difference between the largest and smallest rest mass could be almost as large as 320 meV, say 319 meV, and as small as a very small number, say perhaps 1 meV. If I am incorrect in my interpretations, I hope someone will post an explanation about my errors. Does anyone know of any other similar experiments, or theory, that would substantially narrow the range of possible differences between the largest and smallest rest mass?