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A glass-enclosed photomultiplier with local digitization: pulse times and charges enter event reconstruction. Reciprocal electrical pulses synchronize module clocks to the surface time base.^[ref]

Weak charged current interactions of muon neutrinos usually give extended muon tracks. Compact particle showers occur in other channels, including weak neutral current interactions of every neutrino flavor. Tracks generally constrain direction better; escaping particles complicate energy inference.^[ref]

The Homestake experiment, led by Raymond Davis Jr., used electron neutrino capture on chlorine to produce argon subject to radioactive decay. The 1968 paper reported an upper limit, rather than a resolved positive signal.^[ref]

The underground target contained tetrachloroethylene. Circulated helium swept out argon, which was trapped on cooled charcoal, purified, and put into tiny proportional counters. Electron capture back to chlorine supplies the delayed readout. Added stable argon checked extraction recovery; background counting checked spurious pulses. The capture threshold is $0.814\mathrm{MeV}$ and the product's half-life is about 35 days. The chemical extraction retains neither the original neutrino's arrival time nor its direction.^[ref]

The reaction selects electron neutrinos, and its threshold excludes the lowest-energy part of the solar neutrino spectrum. A low count alone cannot distinguish a low source neutrino flux, a changed neutrino flavor mixture, or an underestimated loss in extraction or counting. This is why chemical recovery tests and an independent water Cherenkov neutrino reconstruction are scientifically valuable.

How can a detector establish that an unseen particle changes identity? The Super-Kamiokande atmospheric-neutrino experiment compares different travel paths; the Sudbury Neutrino Observatory compares different interaction channels. Both infer neutrino flavor from reaction products and calibrated responses. Their complementarity connects particle detection to neutrino oscillation, neutrino mass and neutrino astronomy.

Takaaki Kajita and Arthur B. McDonald shared the 2015 physics Nobel Prize. These were collaboration achievements: Yoichiro Suzuki's Super-Kamiokande work included the solar neutrino analysis, and George Ewan helped establish and lead the Sudbury Neutrino Observatory.^[ref][ref]

The older Kamiokande account explains water Cherenkov neutrino reconstruction; Raymond Davis Jr.'s Homestake experiment explains why a deficit in an electron neutrino channel alone leaves a source-versus-propagation ambiguity. Complementary channels can break that ambiguity.

Kamiokande, associated with Masatoshi Koshiba, was an underground water Cherenkov detector viewed by photomultipliers. Improved water purity and reduced background enabled solar neutrino observations. A concentration of reconstructed recoil directions toward the Sun distinguished a source signal above an approximately direction-independent background.^[ref]

For solar neutrinos, Electron elastic scattering supplies a directional recoil, with different cross sections for active neutrino flavors. Neither the Homestake experiment deficit nor the SN 1987A neutrino burst alone established neutrino oscillation; later evidence compared complementary channels and propagation effects.^[ref]

Use natural units $c=1$ and the Minkowski metric with signs $(+,-,-,-)$. In the ideal centre-of-momentum frame, assume a known initial four-momentum $P=(\sqrt{s},0)$, no unaccounted radiation and exact visible reconstruction. DefineThe missing four-momentum in electron-positron collisions is a subtraction of measured quantities. It is not itself a particle detector hit. With $M_{e\mu }^2=(p_e+p_{\mu }{)}^2$, expansion gives the useful identityFor any collection of future-directed massless invisible four-momenta $q_i=E_i(1,{\hat{\mathbf{n}}}_i)$,Thus a positive missing invariant mass excludes exactly one massless invisible particle under the stated assumptions. It does not exclude one massive invisible particle, identify a neutrino flavor, or determine the number of massless invisible particles beyond that lower bound. Several collinear massless particles can even have zero combined invariant mass. Detector resolution and unaccounted radiation invalidate a literal event-by-event interpretation of these ideal inequalities.

For an original exact example in natural units, choose total energy $6\mathrm{GeV}$ and visible massless four-momenta, in $\mathrm{GeV}$,Two possible invisible massless four-momenta are $(2;-1/2,-1/2,\sqrt{14}/2)$ and $(2;-1/2,-1/2,-\sqrt{14}/2)$. Splitting either into two positive collinear parts gives a three-particle interpretation with identical recoil. Alternatively, one invisible particle of mass $\sqrt{14}\mathrm{GeV}$ has that recoil. This example tests the ambiguity of the subtraction, without asserting any of these alternatives is a tau lepton decay.

Neutrino astronomy infers properties of astronomical sources from detected neutrino reactions. Solar neutrino detection probes ongoing stellar nuclear fusion; the SN 1987A neutrino burst probes a brief episode of core-collapse supernova evolution. A detector observes reaction products, so source inference depends on cross sections, neutrino flavor, thresholds and detection efficiency.

The mass of a neutrino mass eigenstate. A neutrino flavor need not have one definite mass; neutrino oscillation probes differences of squared masses.

Neutrino oscillation is coherent conversion between neutrino flavors: different mass eigenstates acquire different propagation phases. It measures squared-mass differences and mixing, rather than an absolute neutrino mass. The Super-Kamiokande atmospheric-neutrino experiment tests path-dependent disappearance; the Sudbury Neutrino Observatory compares reactions with complementary neutrino flavor sensitivity. Solar neutrino propagation also requires matter effects; the two-flavour vacuum survival model is only an illustration.

The SNO Collaboration used $1000$ tonnes of heavy water in a $12\mathrm{m}$ acrylic sphere, surrounded by ordinary water shielding and $9456$ photomultipliers. Weak charged current (CC) breakup of a deuteron selects electron neutrinos; weak neutral current (NC) breakup measures all active neutrino flavors; Electron elastic scattering (ES) has reduced non-electron sensitivity.^[ref]

The neutrino flavor associated with the tau lepton in the weak charged current. Its direct detection through interactions producing a tau lepton was announced by the DONUT experiment in 2000.^[ref]

For a deliberately simplified neutrino oscillation calculation, take two neutrino flavors related to two mass eigenstates by a real rotation matrix with angle $\theta$. A quantum superposition acquires different phases during propagation; projecting back onto the initial neutrino flavor gives the probabilityHere $L$ is path length and $E$ is neutrino energy; the numerical coefficient incorporates unit conversion.

The paper states the corresponding conversion formula.^[ref]

The path dependence has a geometrical origin. In an original spherical-Earth model, let $R$ be the radius and $h$ a fixed production height, neglecting detector depth. Let $\Theta$ be the zenith distance of the direction in the sky from which the neutrino arrives, so $c=\cos \Theta =+1$ means downward propagation. The backward ray from detector to production obeys $R^2+L^2+2RLc=(R+h{)}^2$. Its positive solution isThus $L(+1)=h$ and $L(-1)=2R+h$. The calculation explains why opposite directions test very different baselines, rather than attributing every observed direction to the same travel distance. Actual production heights and the angle between the outgoing charged lepton and incoming neutrino smear that relationship.

For an original chosen example, set $\theta =\pi /4$ and $\Delta m^2=2.5\times 10^{-3}{\mathrm{eV}}^2$. At $E=1\mathrm{GeV}$, $L=20\mathrm{km}$ gives $P_{\mu \mu }\simeq 0.9960$, while $L=500\mathrm{km}$ gives $P_{\mu \mu }\simeq 0.000279$. The first minimum is at $L/E\simeq 494.7km/GeV$. These are stipulated inputs, not a fit to the 1998 data. A broad distribution of true $L/E$, together with energy and directional uncertainty, smooths the sharp minima.

A direct amplitude check makes the mechanism explicit. DefineThen $S_{11}={\cos }^2\theta +{\sin }^2\theta e^{-2i\phi }$. Taking its squared absolute value yields the displayed survival formula because $1-\cos (2\phi )=2{\sin }^2\phi$. Unitarity gives $|S_{11}{|}^2+|S_{21}{|}^2=1$: disappearance from one channel becomes conversion to the other within this closed model.

This illustration does not describe all solar neutrino propagation. Coherent forward scattering in matter changes the effective propagation operator, and three active neutrino flavors require a larger mixing description. Even in the simplified model, neutrino oscillation measures a squared-mass difference; it does not determine the absolute neutrino mass.