LEPTON

The name lepton derives from the Greek word leptos, meaning thin or light. This name is appropriate because leptons are a set of particles with no measurable dimensions, and hence they are elementary. One of the members of this family, the electron, was the first elementary particle to be discovered. Two other family members that carry electric charge are the muon and the tau. For each of these three charged leptons, there is an uncharged partner particle, a neutrino. There is an electron neutrino, a muon neutrino, and a tau neutrino.

Leptons were discovered much earlier than the other set of elementary fermions, the quarks, because they appear individually in nature rather than as composite particles. The defining feature of a lepton is that it does not participate in the strong interaction, allowing it to exist for substantial periods of time as an independent particle.

The set of leptons can be arranged into three generations, as shown in Table 1. There is an electron, muon, and tau lepton family. Each generation has two particles and two antiparticles, where the antiparticles have the same mass as the particle but opposite quantum numbers.

Each force has an associated charge. By historical convention, the electrically charged leptons are assigned one unit of negative, rather than positive, electric charge. Leptons do not participate in the strong interaction, so it is said that they carry zero strong (color) charge. All fermions participate in the weak interaction and carry weak charge. Through the weak interaction, the more massive charged leptons may decay into their less massive counterparts.

It has been experimentally observed that the net difference in the number of leptons compared to anti-leptons before and after an interaction is unchanged. This is known as lepton conservation, which has an associated quantum number of lepton L . Leptons have L = +1 and antileptons have L = -1, whereas quarks have L = 0. As an example of L conservation, consider the case where an electron and positron annihilate and create a muon and an antimuon (e⁺e^- → μ⁺μ^-). Prior to the interaction L = (+1) + (-1) = 0, and after the interaction L = (+1) + (-1) = 0.

TABLE 1

It is also observed that the net number of leptons and antileptons within each generation is conserved in each interaction. Therefore, a quantum number is introduced for each family: the lepton family number. The reaction e^-e⁺ → μ⁺μ^- has L_e = (+1) + (-1) = 0, L_μ = 0, L_τ = 0 prior to the interaction, and L_e = 0, L_μ = (+1) + (-1) = 0, L_τ = 0 after the interaction and so conserves lepton family number. The only case where lepton family number is violated occurs in the quantum mechanical effect called neutrino oscillations, and in this case the total lepton number L is still conserved.

The charged lepton masses are similar in magnitude to the quark masses. There is no direct evidence that neutrinos have mass. Experiments have only placed upper bounds on the neutrino masses. Neutrino masses are so tiny that direct measurement in the near future will be very difficult. However, it may be possible to infer that neutrinos have mass through the observation of neutrino oscillations, a quantum mechanical effect that can be observed only if each neutrino species has a different mass. In the Lagrangian that describes the fermions, the masses of the charged leptons are arbitrary parameters. The neutrinos are explicitly assumed to be massless.

Assuming that neutrinos are massless provides an explanation for neutrino handedness, a property observed in the weak charged-current interaction. To understand handedness, it is simplest to begin by discussing helicity, since for massless particles helicity and handedness are identical. For a spin-½ particle, helicity is the projection of a particle's spin along its direction of motion. Helicity has two possible states: spin aligned opposite the direction of motion (negative or left helicity) and spin aligned along the direction of motion (positive or right helicity). If a particle is massive, then the sign of the helicity of the particle is frame-dependent. For example, in a frame where one is moving faster than the particle, the sign of the momentum changes but the spin does not, and therefore the helicity flips. However, for massless particles, traveling at the speed of light, one cannot boost to a frame where helicity changes sign so helicity is conserved.

Handedness (or chirality) is the Lorentz invariant (i.e., frame-independent) analogue of helicity for both massless and massive particles. There are two states: left-handed (LH) and right-handed (RH). For the case of massless particles, including Standard Model neutrinos, helicity and handedness are identical. A massless fermion is either purely LH or RH and, in principle, can appear in one or the other state. Massive particles have both RH and LH components. It is only in the high-energy limit, where particles are effectively massless, that handedness and helicity coincide.

Unlike the electromagnetic and strong interactions, the weak interaction has a definite preferred handedness. In the late 1950s, in Madam Wu's famous parity violation experiment, it was shown that neutrinos are LH and antineutrinos are RH. No RH neutrino interactions or LH antineutrino interactions have ever been observed.

RH neutrinos (and LH antineutrinos) could in principle exist but be undetected because they do not interact. Neutrinos do not interact via the electromagnetic interaction because they are neutral or via the strong interaction because they are leptons. In addition, the RH neutrinos do not participate in the left-handed weak interaction. Because RH neutrinos are noninteracting, these hypothetical leptons (not a part of the Standard Model) are called sterile neutrinos.

They raise obvious theoretical and experimental questions. From a theoretical viewpoint: how do sterile neutrinos come into existence since they cannot interact? This is solved relatively easily if the Standard Model is extended to include, at energy scales well beyond the range of present accelerators, a right-handed W interaction that could produce the RH neutrino. From a experimental viewpoint: if there are sterile neutrinos out there, how can they be observed if they do not interact? The quantum mechanical effect called neutrino oscillations provides one method—if neutrinos have mass.

See also:Case Study: Super-Kamiokande and the Discovery of Neutrino Oscillations; Experiment: Discovery of the Tau Neutrino; Experiment: g-2 Measurement of the Muon; Neutrino; Neutrino, Discovery of; Neutrino Oscillations; Particle; Quarks; Standard Model

Bibliography

Kane, G. The Particle Garden (Perseus Publishing, Cambridge, MA, 1995).

Ne'eman, Y., and Kirsh, Y. The Particle Hunters (Cambridge University Press, Cambridge, UK, 1996).

Sutton, C. Spaceship Neutrino (Cambridge University Press, Cambridge, UK, 1992).

Janet Conrad

lepton One of a class of elementary particles. There are 12 types, including the electron and electron-neutrino, muon and muon-neutrino, tau and tau-neutrino, together with their antiparticles (anti-leptons). Leptons interact by electromagnetic interaction and are governed by the weak nuclear force, the force involved in radioactive decay. They have no quark substructure.