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The Standard Model of particle physics was built on the assumption that neutrinos have no mass. In 1998 a Japanese physicist stood up at a conference and showed data that broke that assumption. This post covers what Takaaki Kajita found, how the detector saw it, and a worked calculation you can follow with Class 11 trigonometry.
Who is Takaaki Kajita?
His Nobel Prize facts page says he was born on 9 March 1959 in Higashimatsuyama, Saitama, Japan, and that his doctoral adviser was Masatoshi Koshiba, a future Nobel laureate. He has been at the Institute for Cosmic Ray Research of the University of Tokyo since 1988.
His own Nobel autobiography is unusually honest. He spent much of high school and university practising kyudo, Japanese archery, and writes: "I regret that I should have learned more physics during my undergraduate studies, because these studies in undergraduate courses form the basis of everyday research." He received his PhD in March 1986. He was not selected for a national postdoctoral fellowship, and Koshiba offered him a one-year research post. He stayed two years, and he says that this period was when he found the deficit of atmospheric muon neutrinos.
What was the atmospheric neutrino puzzle?
When cosmic rays hit the upper atmosphere they make showers of particles, and the decays produce neutrinos. The Nobel Committee's scientific background explains that physicists expected a fixed ratio of muon neutrinos to electron neutrinos. Detectors reported the observed muon-to-electron ratio divided by the expected one. The IMB experiment found about 0.54 and Kamiokande about 0.60, where 1 would mean nothing missing. Something was removing muon neutrinos, but nobody could say what.
How did Super-Kamiokande catch them?
The Nobel popular science background describes the detector. Super-Kamiokande sits 1,000 metres underground in a zinc mine. It is a tank 40 metres high and as wide, holding 50,000 tonnes of ultra-pure water, watched by more than 11,000 light detectors. Kajita's autobiography records that data taking began at midnight on 1 April 1996.
Almost every neutrino passes straight through. Now and then one hits a nucleus or electron in the water and makes a fast muon or electron, which gives off a faint cone of Cherenkov light. The shape of the light ring shows which kind of neutrino caused it and which direction it came from. Our post on Pavel Cherenkov explains where that light comes from.
What did Kajita show in 1998?
Neutrinos from cosmic rays should arrive equally from all directions, since Earth barely blocks them. Super-Kamiokande could compare muon neutrinos coming down from the sky above with those coming up through the whole planet. According to the scientific background, Kajita presented the result at the Neutrino '98 conference: up-going muon neutrinos were missing, and the deficit depended strongly on direction. Electron neutrinos showed almost no such effect. The collaboration published it as Evidence for oscillation of atmospheric neutrinos in Physical Review Letters.
The explanation is that muon neutrinos change into tau neutrinos as they travel, and the long path through Earth gives them time to do so. Quantum theory allows this change only if the different neutrino states have different masses.
Worked example: why the up-going neutrinos vanish
The scientific background gives the two-flavour formula for the chance that a muon neutrino has become a tau neutrino:
P = sin²(2θ) × sin²(1.27 Δm² L / E)
with Δm² in eV², distance L in kilometres and energy E in GeV. It also gives the mixing angle as about 42°, so sin²(84°) ≈ 0.99, close to 1.
Find Δm² from the data. Super-Kamiokande saw the deepest dip at L/E ≈ 500 km/GeV. The first maximum of sin² comes when its argument is π/2, so 1.27 × Δm² × 500 = 1.571, which gives Δm² = 1.571 / 635 ≈ 2.5 × 10⁻³ eV².
Down-going, 1 GeV. Take a sample path of 20 km of atmosphere. The argument is 1.27 × 0.0025 × 20 = 0.064 radian. sin(0.064) ≈ 0.064, and squaring gives about 0.004. Fewer than 1 in 200 change.
Up-going, 1 GeV. The path is close to Earth's diameter, about 12,700 km. The argument is 1.27 × 0.0025 × 12,700 ≈ 40 radians. With real spreads in energy and direction, sin² swings so fast that it averages to one half. About half the muon neutrinos have changed type.
That is the up-down difference Kajita showed.
Common mistakes: using degrees instead of radians inside the sine, and forgetting that P is a probability for each neutrino, not a fraction of energy lost.
Neutrino oscillation is not in the JEE (Main) 2026 syllabus, but the idea behind it, two waves of slightly different frequency drifting in and out of phase, is the same physics as beats. The Fermi Simulation Lab has interactive simulations for ideas that are easier to see than read, which helps when superposition feels abstract.
What can a student take from Kajita's way of working?
Small anomalies deserve attention. A ratio of 0.6 instead of 1 had several possible causes. Direction was the test that separated them.
Build the comparison into the experiment. Up-going and down-going neutrinos were measured in the same tank, so most errors cancelled.
A setback is not the end. He missed a fellowship and found the deficit while on a short contract. For the first part of the story, read our post on Reines and Cowan's neutrino detection.
Next step: redo step 3 with E = 10 GeV and see how the argument, and the answer, change.
