Deep-dive paper
Evidence for oscillation of atmospheric neutrinos
The measurement that showed atmospheric neutrinos change flavour on their way to the detector — and therefore carry mass.
Why it matters
P(t) treats the ambient flux Φ as a real, continuously present physical field. That premise only holds if neutrinos are genuine massive particles rather than a bookkeeping fiction. This result settled the question.
Method
A 50,000-tonne water Cherenkov detector recorded neutrinos produced by cosmic-ray collisions in the atmosphere, comparing those arriving from overhead with those that had travelled through the whole Earth.
Mechanism
Because oscillation probability grows with travel distance, up-going and down-going muon neutrinos should differ if neutrinos have mass. A clear up–down asymmetry appeared exactly as oscillation predicts.
Results
Muon-neutrino events were depleted for long baselines, consistent with νμ oscillating into another flavour, implying a non-zero mass-squared difference of order 10⁻³ eV².
Significance
It converted neutrinos from a hypothetical into an established, massive constituent of the ambient environment, and earned a share of the 2015 Nobel Prize in Physics.
Formula-term mapping
Directly supports Φ(E,θ,t): a real, directionally structured, ever-present neutrino flux is what the flux-density term integrates over.