The origin and status of the third neutrino

Abstract

1. The three lepton families The elementary particles known today fall in two categories: twelve spin particles (fermions), the building blocks of matter, and twelve spin 1 particles (bosons), which are the mediators of all the forces but gravity. The last element in the Standard Model is a spin 0 particle, thought to be at the origin of the masses and called the “Higgs” after the name of one of the discoverers of the theory. Not yet detected, it is searched for at the new CERN LHC collider. The fermions come in three different groups, called families, of identical structure. The reason for that is unknown. Each family is made of a doublet of quarks, of charge +2/3 q and –1/3 q (q is the proton charge), and a doublet of leptons, one of charge –q and one neutral. The neutral leptons are collectively called neutrinos, but are three different particles, distinguished by an additive quantum number called “lepton flavour”. The electron (e) and the electron-neutrino ( e) have one unit of electronic flavour (–1 their antiparticles); the muon ( ) and the muon-neutrino ( μ) have one unit of muonic flavour and similarly for the tau ( ) and the tau-neutrino ( ). The charged leptons are distinguished by their masses (increasing with the family number) and lifetimes, neutrinos only by their lepton flavours. Neutrinos are produced in states of definite flavour, as e, μ or , in pairs with an antiparticle of the same and opposite flavour. Elementary interactions conserve flavours. So that, by definition, the electron-neutrino ( e) is the neutral lepton produced with a positron (e), the μ is the one produced with a + and the is the one produced with a . And electron-anti-neutrino is the neutral particle produced with an e, etc. Neutrinos cannot be detected directly. However, when one of them interacts with the matter producing a charged lepton, the latter can be detected. The identification of the charged lepton gives the flavour of the neutrino: if it is an electron (e) it was a e etc. Experiments show that neutrinos born with a flavour produce charged leptons of the same flavour, provided the ratio L/E between distance from production to interaction points and neutrino energy is not very large, namely if the oscillation phenomenon has no time to develop. Indeed, experiments in underground laboratories have shown that neutrinos do not behave as assumed in the Standard Model, they do change, “oscillate”, between one flavour and another. The evidence has gradually grown in the last four decades, by studying the es produced by the fusion reactions in the core of the Sun and the μs indirectly produced by the cosmic rays collisions in the atmosphere. Confirmations came by experiments with artificial neutrino sources: proton accelerators (producing mainly μ) and nuclear power reactors ( e ). There two types of experiments. In a disappearance experiment the flux of neutrinos of a certain flavour is known at production; if the flux is measured at a (large) distance and found to be less than expected, the oscillation to another flavour is inferred. In an appearance experiment a flavour not present at production is searched. Oscillations happen because neutrinos of definite flavour are not stationary states (mass eigenstates). The latter, 1, 2 and 3, do not change and have definite masses, m1, m2 and m3. The two basis are linked by an orthogonal transformation that can be expressed in terms of three rotations, through angles that we shall call 12, 23 and 13, and of phase factors. If neutrinos are Dirac particles, as assumed in the Standard Model, all but one of the phase factors can be absorbed, as in the case of quarks, in the wave functions of the states. However, neutrino and antineutrino might be two states of the same particle, namely ‘Majorana particles’. In this case two more phases, which we shall call M