Leptons and Antileptons

In 1961, some experimental results providing support for this picture of the proton and the neutron were reported by Robert Hofstadter and his CO workers at Stanford University and by a group of investigators at Cornell University. These physicists studied the scattering of high-speed electrons by protons and neutrons, and were able to interpret their experiments to determine the distribution of electric charge with the proton and the neutron. 

These results about the structure of the nucleon give exciting promise of great future developments in the understanding of the fundamental nature of the universe. 

We begin the tabulation of the fundamental particles by discussing the leptons and antileptons. There are eight of these particles known. Some of their properties are given in Table 20-1. Except for the muon and antimuon, they are stable particles. The word lepton is from the Greek leptos, small. 

Name Electric Charge Mass Xenicity (strangeness) Spin 

The muon, /jl, was the first particle with mass intermediate between the electron and the proton to be discovered. It is present in cosmic rays. It is made by the following reaction  

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The baryons, antibaryons, leptons, and antileptons are all fermions. Particles with spins f, t,. . . are also fermions. 

In these examples, the guiding principle is the principle of lepton number conservation. In any process, the total number of leptons and antileptons does not change the number before and after is conserved. Table I lists the assigned lepton numbers for each lepton family. The lepton number is positive for a lepton and negative for an antilepton. By applying the lepton numbers for the electron family, the principle of lepton conservation is exhibited in the three examples given. 

Pauli proposed that two particles were emitted, and Fermi called the second one a neutrino, V. The complete process therefore is n — p -H e 9. Owing to the low probabiHty of its interacting with other particles, the neutrino was not observed until 1959. Before the j3 -decay takes place there are no free leptons, so the conservation of leptons requires that there be a net of 2ero leptons afterward. Therefore, the associated neutrino is designated an antineutrino, 9-, that is, the emitted electron (lepton) and antineutrino (antilepton) cancel and give a net of 2ero leptons. 

Second Quantized Description of a System of Noninteracting Spin Particles.—All the spin particles discovered thus far in nature have the property that particles and antiparticles are distinct from one another. In fact there operates in nature conservation laws (besides charge conservation) which prevent such a particle from turning into its antiparticle. These laws operate independently for light particles (leptons) and heavy particles (baryons). For the light fermions, i.e., the leptons neutrinos, muons, and electrons, the conservation law is that of leptons, requiring that the number of leptons minus the number of antileptons is conserved in any process. For the baryons (nucleons, A, E, and S hyperons) the conservation law is the... 

Here L = — 1 on both sides of the equation where we assign lepton numbers of +1 for every lepton and — 1 for every antilepton (e+ is an antilepton). By contrast, the... 

In all reactions the lepton number must be conserved the total number of leptons minus antileptons on each side of a decay or reaction process must be the same. A similar law is valid for the quarks. In the reaction above several quantum numbers are obeyed (i) the charge is the same on both side, (ii) the lepton number is zero on both sides (none = electron minus anti-neutrino), (iii) the quark number is conserved. The elementary reactions in Figure 10.4 can all be described in terms of lepton and quark transformations. 

Leptons, which include the electron, the neutrino, and the muon, have lepton number +1, and antileptons have lepton number —1 all other particles have lepton number 0. There is rigorous conservation of the lepton number in all reactions. 

Solution On the left-hand side of the equation we assume that we have a 24Na nuclide (with 11 electrons) and a single positron, which is an antilepton. The conservation rules imply that the mass number of the product will be 24, the atomic number will be Z= 11 + 1, the 11 electrons will carry over, and an antilepton has to be created to conserve lepton number. Thus,... 

These reactions, called inverse (3 decay, were obtained by adding the antiparticle of the electron in the normal (3 decay equation to both sides of the reaction. When we did this we also canceled (or annihilated) the antiparticle/particle pair. Notice that other neutrino-induced reactions such as ve + n —> p+ + e do not conserve lepton number because an antilepton, ve, is converted into a lepton, e. Proving that this reaction does not take place, for example, would show that there is a difference between neutrinos and antineutrinos. One difficulty with studying these reactions is that the cross sections are extremely small, of order 10-19 bams, compared to typical nuclear reaction cross sections, of order 1 barn (10—24 cm2). 

We have mentioned that the Drell-Yan analysis above refers to the continuum production of lepton-antilepton pairs, and that any events where the lepton pair originates from a heavy meson resonance should be subtracted out before comparing theory and experiment. We now consider lepton pair production via a resonance. In fact, we have already studied this question in Section 5.3.1 in connection with the production and detection of and in pp collisions, but we then neglected all details of the parton model. 

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