DONUT — the tau neutrino had to leave a kink

The 1989 measurement of the invisible decay width of the Z boson at LEP told the world there were three light neutrinos and only three. By that point the electron neutrino had been seen by Cowan and Reines in 1956 and the muon neutrino by Lederman, Schwartz and Steinberger in 1962. The tau neutrino was, by 1989, the only Standard-Model fermion never to have been observed in its own right. Everyone was sure it existed — the tau lepton had been discovered by Martin Perl in 1975, the LEP counting was unambiguous, and the missing energy in tau decays pointed unmistakably to a third neutrino species — but no detector had ever recorded a tau neutrino producing a tau on the spot. The intellectual situation was uncomfortable. The world needed to actually see one.

The reason it had not been done was that tau neutrinos are very hard to make and very hard to detect. To make them you need a source whose primary decays produce charged taus — and the most efficient sources are heavy-flavour mesons, especially D_s, whose leptonic decays D_s → τν_τ produce a tau plus a tau antineutrino. A high-intensity hadron beam on a thick tungsten dump produces D_s in modest numbers, and most of the D_s decay before they can re-interact. The result is a tertiary beam of ν_τ at the level of a tiny fraction of the dominant ν_μ and ν_e flux. The Fermilab Tevatron's 800 GeV proton beam, fired into a tungsten beam dump in the early 1990s, produced roughly one tau-neutrino interaction per kilogram of target per month at the downstream detector — many orders of magnitude below the other neutrino species.

Why the only signature is a kink

Detecting that interaction once it has happened is harder still. The tau lepton lives for about 0.29 picoseconds in its own rest frame, with cτ ≈ 87 micrometres. In the lab frame a tau produced by a 30 GeV neutrino is Lorentz-boosted by a factor γ ≈ 17, so it travels roughly 1.5 millimetres before decaying. After that it disappears into an electron or a muon or one or three pions, plus one or two daughter neutrinos that carry away the kinematic information. From a track point of view the signature is unique: a charged particle appears at the neutrino interaction vertex, travels a few hundred micrometres to a few millimetres in a straight line, and then suddenly changes direction at the decay point. This sudden bend is the "kink." There is no other Standard-Model process that mimics it cleanly, because there is no other charged particle with the right combination of submillimetre lifetime and pointlike production from a neutrino interaction.

The only tracking technology with the spatial resolution to register a kink that small is nuclear emulsion — gelatin sheets loaded with silver-bromide grains roughly a micrometre across, which record the passage of any charged particle with sub-micron precision after chemical development. Emulsion has been used in particle physics since C. F. Powell's discovery of the pion in 1947, but the price of its resolution is that you have to develop it after exposure and scan every track by hand or with a high-throughput microscope. The DONUT spectrometer used 256 modules of emulsion sandwiched with 1-mm steel plates and stainless-steel changeable sheets, a fiducial mass of about 260 kg in total. Downstream of the emulsion stack a conventional magnetic spectrometer measured the charges and momenta of outgoing charged particles, providing the link between the microscopic emulsion tracks and the macroscopic event reconstruction.

Slide the energy up. The kink walks downstream. At 5 GeV it is barely separated from the interaction vertex; at 30 GeV — typical of the DONUT events — it sits about 1.5 mm from the vertex, comfortably resolved by emulsion's micron-scale tracking; at 150 GeV the tau has time to leave the emulsion sheet entirely before it decays, and the geometric link to the interaction vertex becomes the limiting systematic. There is a narrow window of energies — roughly 5 to 100 GeV — in which the kink topology is the unique, clean signature of a tau lepton produced in a neutrino interaction. DONUT was built specifically to land its tau-neutrino events inside that window.

Four events

After three years of exposure at the Fermilab beam dump and three more years of scanning roughly 6 million microscope frames of developed emulsion, the collaboration reported in July 2000 four events whose topology matched the kink signature and whose kinematics were inconsistent with the much more common ν_μ or ν_e charged-current interactions. The expected background from charm-meson decays mimicking the tau was estimated at 0.34 events. The fluctuation probability that the four events were a background fluke was below 4 × 10⁻⁴ — well above the 5σ threshold conventionally required for discovery. Reanalysis of the full data set, published in 2008, brought the count to nine events on a background of about 1.5, settling the case.

The result did not change anyone's belief about whether the tau neutrino existed — that had been settled, indirectly, for over a decade. What it changed was the empirical status of the Standard Model's matter content. The three families of charged leptons and the three families of quarks had been observed in their own right since the discovery of the top quark in 1995. After DONUT, every elementary fermion in the Standard Model had been produced and detected directly. There was no longer any particle whose existence rested only on bookkeeping.

What came after, and what it set up

The DONUT design was small-statistics and accelerator-based. Its successors moved in two directions. The first was the OPERA experiment, which fired the CNGS muon-neutrino beam from CERN to the Gran Sasso laboratory 730 km away and looked for tau leptons appearing from ν_μ → ν_τ oscillation in flight. OPERA reported its first ν_τ candidate in 2010 and ten candidates by 2018, establishing tau appearance from oscillation at 6.1σ — a complementary measurement that used the same emulsion-kink topology to confirm the atmospheric oscillation channel directly rather than inferring it from ν_μ disappearance. The second was the realisation that ν_τ at much higher energies, from oscillation of astrophysical neutrinos, can be detected by their characteristic "double bang" signature in optical Cherenkov arrays — the topology that IceCube uses today.

For the broader context of the three-flavour mixing whose third member DONUT completed, see the PMNS matrix as a 3D rotation; for the indirect counting that fixed the number of light neutrino species over a decade before DONUT directly saw the third one, see how many neutrino flavours.