The tree-level massless character of the neutrino means that its Compton Radius Vortex is probably effectively as large as our universe. This overpowers the surface potential of the Sun by almost a factor of 10. Results from the COBE data suggest that the dominant local background potential is very close to this value. 800 MeV protons hit a beam-stop and produce neutrons and pions. Such a theory would help to explain the apparent shortfall of neutrinos coming from the Sun.
Some tests find tentative but ambiguous evidence for oscillation.
They study neutrinos made when cosmic rays from outer space strike the upper atmosphere. Some neutrinos, those made overhead above Japan, travel about 20 km or so before entering the underground detector. Other neutrinos, those made in the atmosphere on the far side of the globe, have a travel path of 12,700 km into the detector. A 1-GeV muon neutrino seems to oscillate every few hundred miles. This does not yield a value of the masses themselves, only of the difference between those of muon neutrinos and other types.