neutrino mass ordering

We know neutrinos come in three mass states, and oscillation has told us the gaps between their squared masses — but not which one sits on top. Picture three rungs of a ladder whose spacings you have measured precisely, yet you cannot tell whether the closely spaced pair is at the bottom or near the top. That open question is the neutrino mass ordering: in what order are the three masses stacked?

There are two possibilities. In the 'normal ordering,' the two states with the small solar splitting are the two lightest, and the lone state separated by the big atmospheric splitting sits on top — light, light, then heavy. In the 'inverted ordering,' that lone state is instead at the bottom — so two heavy states with a small gap sit above a single lighter one. Oscillation measurements alone struggle to distinguish the two, because they mostly fix the sizes of the gaps, not the sign of the big one. Clever experiments exploit how neutrinos passing through the Earth feel matter slightly differently in the two cases.

Resolving the ordering matters for several reasons. It feeds directly into searches for neutrinoless double beta decay, whose expected rate depends on the arrangement; it sharpens predictions for the absolute neutrino masses; and it constrains theories that try to explain why neutrino masses are so tiny. Long-baseline accelerator experiments and large underground detectors are closing in on the answer, which is expected to be settled within the next several years.