Before going into the details of neutrino oscillations, I'll discuss some of the basic properties of neutrinos and neutrino interactions. This will lay the groundwork for discussing the theory and observation of neutrino oscillations, and understanding the implications.
The neutrino was first postulated by Pauli in 1930 to account for the observed energy spectrum of electrons from β-decay. By 1930, the basic structure of atoms was understood, electrons orbit a nucleus composed of protons and neutrons, the number of protons determining the chemical structure of the atom. It was also understood that a nucleus can change from one type to another through processes of α or β emission. In β-decay, an electron (or positron) is emitted, and the charge of the nucleus changes by +1 (-1) when a neutron (proton) transforms into a proton (neutron). For example, Strontium-90 (9038Sr) β-decays with the emission of an electron and becomes Yttrium-90 (9039Y).
In β-decay, the initial and final nuclei have well defined mass, and therefore, well defined energies. Yet, the electrons that emerge have a spectrum of energies ranging from zero (as small as can be detected) to a maximum value dependent on the nucleus. For Strontium-90, the maximum electron energy is 0.546MeV. There are no accompanying x-rays or gamma rays. The recoil of the nucleus can't account for the spread of energies. Was energy not conserved in β-decay, or was there something unseen?
To account for the missing energy, Pauli postulated the existence of an unobserved particle and called it the neutrino. To fit with the known facts, the neutrino had to be neutral, of very small mass, and very weakly interacting. In 1934, Fermi proposed a theory for β decay, known as the four-fermi theory (because the interaction coupled four-fermions, not because it was his fourth theory!). The coupling constant in this interaction is GF = 1.16×10-5GeV-2, significantly smaller than α=1/137.
But are neutrinos real, or just an interesting theoretical construction that saves the principle of conservation of energy? Proving the existence of neutrinos took another 25 years. In 1956, Reines and Cowan observed "inverse β-decay", that is, the interaction of an anti-neutrino with a proton yielding a neutron and a positron:
Helicity, or handedness of a particle is the projection of the particle's spin along its direction of motion. For massless particles, the direction of motion is a relativistic invariant, making it a useful concept. For massive particles, the usefulness of helicity depends on the velocity of the particle, especially the velocity of a decay product in the rest frame of the decaying particle.
In 1956, the theorists Lee and Yang pointed out that the weak interactions may violate parity. There was no experimental evidence to the contrary and some (K+ decays to 2π and 3π) to suggest that parity was violated. In 1957, Wu carried out an experiment that proved that weak interactions violate parity, and showed that the violation was maximal (read Sec. 7.5 for more details). In this case, maximal parity violation means that the W± and Z0 couple only to left-handed particles and right-handed anti-particles.
Massive particles are never 100% left-handed or right-handed, but rather a mixture. The relative amount are proportional to β=v/c, and 1-β. For the (nearly) massless neutrinos, helicity is a (nearly) conserved quantity.
With the discovery of new charged leptons, μ and τ, new neutrino types were needed to explain the behavior of their decays. If a muon decays to an electron and a neutrino, then the electron energy in the muon rest frame is fixed (this is a common property of two-body decays). However, the electron energy is seen to vary over a wide spectrum, indicating that this is a three body decay. The obvious temptation is to add a second neutrino, make one an electron type and the other a muon type, and impose conservation of lepton number by type: