Antileptons

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... 

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). 

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. 

Inflation also distorts the mass budget of the universe so badly that less than 1% of the total mass appears visible, but this is the total mass that neatly balances the large-number coincidences of the anthropic principle. The excess must therefore be non-baryonic matter, for which there is no evidence. At the same time, the equal mass of antibaryons, implied by CPT symmetry, is declared non-existent. Antileptons are simply ignored. 

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

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. 

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. 

Other possibilities that have been considered in the literature are that T could be a new lepton with (i) the quantum numbers of either the electron or the muon (this has occasionally been referred to as the ortholepton hypothesis)—in this case the r neutrino, i>r would be identical with either i/g or (ii) with the quantum numbers of one of the light antileptons (the paralepton hypothesis)—in this case would be identical with either z7g or i. All these hjq>otheses have by now been dismissed on experimental grounds. 

The mass m of the lepton-antilepton pair is simply given by... 

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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