Lepton Family Number Conservation
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| Lepton Family Number Conservation
One of the tenets of the current formulation of the Standard Model of particle physics is the conservation of lepton family number. That means little or nothing without further explanation. 1. The leptons as we know them (and have now observed them all) are:
2. The lepton family number is an arbitrary assignment of a value to assist us in keeping track of the number of leptons and anti-leptons. 3. Each lepton has its own anti-lepton: (e-, e+), (-, +), including the neutrinos. 4. If the lepton family number is assigned the value +1, that lepton is called the "particle" and the corresponding lepton with 1 is called the "anti-particle". 5. There are known to be three separate families of leptons: a. The electrons, including the electron-neutrinos b. The muons, including the muon-neutrinos c. The taus, including the tau-neutrinos
b. The total number of muon-type leptons (including their muon-type neutrinos) is a constant. c. The total number of tau-type leptons (including their tau-type neutrinos) is a constant. and, these numbers are conserved separately! So, let's take the familiar neutron decay: 
Because there are no electron-type leptons in the initial state (the neutron is a nucleon which is one member of the baryon family) there can be no net electron-type leptons in the final state. Therefore, if a e() is created in the final state, we need also to create an anti-electron-type lepton in the final state so that the sum of the sum of the lepton numbers for that family remains unchanged in the reaction. Hence, there is an electron-type anti-neutrino created. This particle conserves not only lepton family number as it should according to the standard model, but it also conserves charge and energy and linear momentum and angular momentum, etc. [Note, as an aside, that baryon number is also a required conservation in the standard model, and in these decays we are investigating, it implies that if we begin with (N + Z = A) baryons (nucleons) in the initial state, we need to have A baryons (nucleons) in the final state.] 7. For any reaction (or decay) it is possible to create an analog reaction by moving a particle from one side of the reaction to the other side of the reaction by changing it from it's present particle type to the corresponding anti-particle. So, for example, if a positron appears on the right hand side of the reaction, it is possible to move it to the left side of the reaction and conserve all of the relevant quantities by simply replacing it by its anti-particle, in this case, the electron. Try it: it will conserve charge, lepton family number, etc. Now, in the context of Problem 9.9, you will need to apply lepton family number conservation if you are to determine the proper particle(s) to be included in the reaction. [Note: Krane does not make the distinction between electron-type neutrinos and muon-type or tau-type neutrinos because he does not need to do so here for ordinary radioactivity. So, you should assume that the neutrinos he notes are all electron-type neutrinos for this problem.] I hope this is helpful. Contact me if you have questions. Now, here is something for you to consider. In the laboratory, you are studying muon decay. We know from direct observation that a muon decays into a positron and...? Complete the following equation:  |
