{ 1{ Neutrino Mass

Written February 1998 by B. Kayser (NSF). While there is no unequivocal evidence for neutrino mass, it is natural to suspect that the neutrinos, like the charged leptons and the quarks, have nonzero masses. Evidence of these masses is being sought through experiments on neutrinos created astrophysically, in the earth's atmosphere, by accelerators, by reactors, and by nuclear decays, and in studies of reactions where neutrinos appear only as virtual particles. In the decay W + ! ` + ` (1) of a W boson into a charged lepton of \\avor" `(e; ; or), the accompanying neutrino is referred to as`, the neutrino of avor`. Neutrinos of diierent avor are diierent objects. When an energeticùndergoes a charged-current weak interaction, it produces a charged leptonòf the same avor as the neutrino 1]. If neutrinos have masses, then a neutrino of deenite avor, ` , need not be a mass eigenstate. Indeed, if leptons behave like quarks, thè is a coherent linear superposition of mass eigenstates, given by (2) Here, the m are the mass eigenstates, and the coeecients U `m form a matrix U known as the leptonic mixing matrix. There are at least three m , and perhaps more. However, it is usually assumed that no more than three m make signiicant contributions to Eq. (2). Then U is a 33 matrix, and according to the electroweak Standard Model (SM), extended to include neutrino masses, it is unitary. The relation (2) means that when, for example, a W + decays to an e + and a neutrino, the neutrino with probability jU e1 j 2 is a 1 , with probability jU e2 j 2 is a 2 , and so on. This behavior is an exact leptonic analogue of what is known to occur when a W + decays to quarks. If each neutrino of deenite avor is a coherent superposition of mass eigenstates, then we will have neutrino oscillation 2].