How many neutrinos should exist ?

The SM assumes three types of neutrinos. However, these authors analyzed data to demonstrate the need of two more types [http://www.nature.com/nature/journal/v478/n7369/full/478328a.html?WT.ec_id=NATURE-20111020].

Neutrino oscillations, observed through the transmutation of neutrinos of one type into neutrinos of another type, occur if there is mixing between neutrino types and if individual neutrino types consist of a linear combination of different neutrino masses. (At present, the masses and mixings of the fundamental quarks and leptons can be measured but are not fully understood.) In the case of two-neutrino mixing — for example, mixing between the muon neutrino and the electron neutrino — the probability (P) that a muon neutrino (ν_μ) will oscillate into an electron neutrino (ν_e) is given by P(ν_μ ν_e) = sin²(2θ)sin²(1.27Δm²L/E). Here, θ, in radians, describes the mixing between the muon neutrino and electron neutrino; Δm² is the difference of the squares of the masses of the two neutrinos in square electronvolts; L is the distance travelled by the muon neutrino in kilometres; and E is the muon-neutrino energy in gigaelectronvolts.

In general, the number of different neutrino masses equals the number of neutrino types, so that three-neutrino mixing involves three neutrino masses and two independent Δm² values, whereas five-neutrino mixing involves five neutrino masses and four independent Δm² values. Neutrino oscillations have been observed at a Δm² of about 7 × 10⁻⁵ eV² by detectors that measure the flow of neutrinos from the Sun and experiments that detect neutrinos at a long distance from nuclear reactors. The oscillations have been detected at a Δm² of around 2 × 10⁻³ eV² by detectors that measure the flow of neutrinos from the atmosphere and by experiments in which neutrinos are measured at a long distance from particle accelerators. In addition to these confirmed observations of neutrino oscillations, there is also evidence for oscillations at a Δm² of about 1 eV² from short-distance accelerator and reactor neutrino experiments^{2, 3, 4}. However, it is not possible to explain this third Δm² value with only three neutrino masses. Therefore, additional neutrino masses are required.

In their study, Kopp et al.¹ tried fitting the world neutrino-oscillation data to theoretical models involving four different neutrino masses (three active neutrinos plus one sterile neutrino) and then five different neutrino masses (three active plus two sterile neutrinos; Fig. 1). They found that one sterile neutrino was insufficient to explain the world data, but two gave a satisfactory global fit. (Similar fits are discussed elsewhere^{5, 6, 7, 8, 9, 10}.) One other feature of the authors' two-sterile-neutrino fit is that it allows for violation in leptons of the charge–parity (CP) symmetry — according to which particles and antiparticles behave like mirror images of each other — or for a difference between neutrino oscillations and antineutrino oscillations. Such CP violation might help to explain the r-process, in which heavy elements are produced through nuclear reactions involving rapid neutron capture (hence the 'r'), and the production of heavy elements in neutrino bursts from stellar explosions known as supernovae. It might also help to explain why the Universe is dominated by matter and not by an equal amount of matter and antimatter.