What is the lepton number of an electron?
We might start off by asking what is the lepton number of anything; or for that matter, what’s a lepton? Let’s start to understand these terms a bit better before we can answer this question. First, because we already have a bit of an idea of what electrons are, let’s talk about what leptons are. A lepton is an elementary particle that has half-integer spin. That may remind us of electrons, and indeed electrons actually are within the class of leptons. There are six different kinds of leptons, and electrons are one of them. But a lepton is not defined only by its half-integer spin; there’s more to it.
Think for a second about the nucleus of an atom consisting of protons and neutrons. We knew that protons have a positive charge and neutrons have no charge. So overall, the charge of this nucleus, this tightly bound cluster of protons and neutrons, is positive. Knowing what we know about electric charge, that like repels like, that raises the question why do nuclei stay together. Why don’t they just push one another apart because of all that positive concentrated charge? The answer comes down to the strong nuclear force, which is a very short range force which helps to overcome that electrostatic repulsion.
We bring up the strong nuclear force because leptons explicitly do not participate in that strong force. That’s something for other types of particles, namely quarks, to participate in. Summarizing this, we can write that a lepton is an elementary particle of half-integer spin that does not engage in the strong force, also called the strong nuclear force. This then gives us an idea about leptons, but what’s this notion of lepton number? When we calculate the lepton number of some particle or system of particles, what we’re doing is we’re counting the number of leptons and we’re subtracting from that the number of antileptons.
Perhaps you’ve heard of protons and antiprotons or electrons and antielectrons. Well leptons have antileptons; that is, particles with properties such as spin or charge that have the same magnitude as their corresponding lepton, but the opposite sign. For example, if we had a lepton that had a spin of positive one-half, then the antilepton corresponding to it would have a spin of negative one-half. Anyway, as we said, the lepton number of a particle is equal to the number of leptons it contains minus the number of antileptons it has.
Now we in this case want to solve for the lepton number of an electron. And we noted earlier that an electron is actually an example of a lepton; it’s one of the six types. So therefore, when we apply our equation for lepton number to the electron, we know that an electron being a lepton has one lepton in it. And that since an electron is purely a lepton, it has zero antileptons. The math then comes out to be fairly simple. The lepton number of an electron is one minus zero, or simply one. That’s the lepton number of an electron, which itself is a lepton.