# Lesson Video: Charm Physics

In this video, we will learn how to determine the charm of composite particles and sets of particles and whether given interactions conserve charm.

14:21

### Video Transcript

In this video, we’re talking about charm. We’re going to see that charm is a property of subatomic particles and also of nuclear equations. We’ll also learn how to calculate the charm of any particle that we’re given. And we’ll do this by understanding the connection between charm and the charm quark.

As we said, in physics, charm is a property of subatomic particles. This means that for a given particle, we can come to know its charm, we say, just as we might know its electric charge or its mass. Charm is directly connected to the quark that goes by that same name. Specifically, if we consider the six quark and antiquark pairs, we can say that for a given particle, its charm is determined by the number of charm quarks and antiquarks it may possess. In fact, we calculate the charm of a particle according to this rule. Every charm quark that a particle possesses contributes a charm, we represent it with a capital C, of positive one to the particle overall. On the other hand, every charm antiquark the particle possesses contributes a charm of negative one.

This means, for example, that the charm of the charm quark is positive one and that of the charm antiquark is negative one. One other point about charm is that it’s only the charm quark and antiquark that contribute to this property. None of the other quark types and their antiparticles or any other particle for that matter affect it. This tells us, by the way, that the only way a given particle can have a nonzero charm is if it has some number of charm quarks or charm antiquarks.

By way of example, imagine that we had a particle made up of two down quarks and one up quark. This, we know, is a neutron. If we wanted to calculate the charm of this neutron overall, we would do it by adding together the charm of each of its three quarks. But then, according to our rule, none of the quarks present in this neutron contribute anything to its overall charm. That just means that the charm of a neutron is zero. But now imagine that we were to take one of these down quarks and replace it with a charm quark. Since the charm of a charm quark is positive one, we would say the charm of our particle overall now is positive one. What we’re seeing is that for a composite particle, the charm of that particle is equal to the sum of the charm of the particles that make it up. With these quarks, that sum is zero plus zero plus one.

At this point, we might wonder, what if this subatomic particle that we want to calculate the charm of is not made up of quarks? For example, what if it’s an electron, say, or a tauon or some sort of neutrino? These particles, we know, belong to a class of particles called leptons. Leptons are not made up of quarks but rather are fundamental particles. As far as we know, they’re not made of anything smaller. If our particle was, say, an electron, what’s the charm of that? Well, helpfully, the same rule applies in all cases. For any particle, whether a lepton or hadron or any other sort, we calculate its charm by adding up the number of charm quarks and charm antiquarks it possesses. And if it doesn’t have any of them, as is the case for all leptons including our electron, then its charm must be zero.

Now, earlier we mentioned that charm is a property of subatomic particles in the same way that mass or electric charge is. And electric charge, for example, is a quantity that we say is conserved across interactions. This means that in any nuclear equation, the total electric charge on one side equals that on the other. When we look at charm across nuclear equations, though, we find that sometimes it’s conserved and sometimes it isn’t. We can clear a bit of space and show this through nuclear equations.

Here, we have a particle called a charmed eta meson decaying into a pion, a neutral kaon, and a negatively charged kaon. To study this interaction from the perspective of charm, we’ll want to look at the quarks that make up each one of these particles. Each of the particles is a meson made up of one quark and one antiquark. If we look first at what we could call the reactant side of this interaction, that includes just the charmed eta meson. This is made of one charm quark, which contributes a charm of positive one, and one charm antiquark, contributing a charm of negative one. Positive one minus one is zero, so that’s the overall charm of this charmed eta meson.

Then, we look at the particles on what we could call the product side of our interaction. As we look at the quarks that make up these three particles, we see that none of them are the charm quark or the charm antiquark. Therefore, the charm of our pion is zero, the charm of our neutral kaon is zero, and so is the charm of our negatively charged kaon. Considering our reactant and product side, we see that the total charm on either side is zero. Therefore, in this interaction, charm is conserved.

But as we mentioned, this isn’t always the case. We now consider this nuclear interaction, where a particle called a charmed lambda baryon decays into a proton, a negatively charged kaon, and a pion. Once again, we’ll look at the charm of these particles. And to do that, we’ll need to look at the quarks that make them up. Note, by the way, that in this interaction, we have two baryons, particles made up of exactly three quarks, and two mesons, particles made of a quark and an antiquark.

Anyway, when we look at the quarks that make up our charmed lambda baryon, we see they include the up, the down, and the charm quark. The up and the down don’t affect the charm of our particle overall, but the charm quark does. It gives it a charm of positive one. Then, as we consider the charm of the proton, we see that this has no charm quarks or charm antiquarks. So, its overall charm is zero. And just like before, that’s true also of the negatively charged kaon and the pion. In this interaction, then, we have a total charm of one on what we could call the reactant side and a total charm of zero on the product side. So, charm is not conserved.

Now, we’ve gone through all this in part so that we can explain the rule for when charm is conserved and when it is not. It actually comes down to which of the four fundamental forces — and we can remember that those forces in decreasing order of strength are the strong nuclear force, the electromagnetic force, the weak nuclear force, and gravity — governs or drives a given nuclear interaction. In some, whenever an interaction is governed by the strong nuclear force or the electromagnetic force, then in that case charm is conserved, as we saw here in our first example. On the other hand, if it’s the weak nuclear force that’s primarily responsible for an interaction, then charm is not conserved, as we saw in the second case. By the way, gravity is left out of this discussion because it’s so much weaker than the other three fundamental forces that it effectively never is the primary force responsible for a nuclear interaction.

So, in such an interaction, if charm is conserved, we know that interaction is governed by either the strong force or the electromagnetic force. If charm is not conserved, then that means the weak nuclear force is responsible. Knowing all this about charm, let’s get some practice now through an example.

A charmed lambda baryon is a baryon with the composition udc. What is the charm of the charmed lambda baryon?

Alright, in this exercise, we’re considering a baryon. This is a particle made up of exactly three quarks, represented by this symbol. We want to calculate the charm of this baryon. And it turns out that we don’t need to recognize this symbol or even know its name in order to calculate this charm. That’s because the charm of a given particle is affected only by the number of charm quarks and charm antiquarks it may possess. As long as we know the quarks a particle is made up of then, we can calculate its overall charm.

And in this case, we’re told the three quarks making up this baryon are the up quark, the down quark, and one charm quark. Our rule for calculating charm tells us that for every charm quark that contributes a charm of positive one to a particle and every charm antiquark contributes a charm of negative one. This baryon, we see, doesn’t have any charm antiquarks, but it does have a charm quark. That by itself contributes a charm of positive one. The up and the down quark, on the other hand, don’t affect the charm of this particle. If we say that the total charm of our baryon is capital C, then this is equal to the charm of our up quark plus the charm of our down quark plus that of our charm quark. This is positive one, so that’s our answer for the charm of the charmed lambda baryon.

Let’s now look at a second example exercise.

A type of omega baryon has the composition ccc. What is the charm of this omega baryon? What is the relative electric charge of this omega baryon?

In this exercise, we’re working with a particle made of exactly three quarks. And we’re told that each one of those quarks is a charm quark. If we were to make a sketch of this baryon then, it would look like this. For this composite particle, we want to know what its charm and its relative electric charge are. Considering the first part of our question, we know that the charm of a particle overall is determined by the number of charm quarks and charm antiquarks it may possess. Every charm quark contributes a charm, we could say, of positive one to the particle, while every charm antiquark contributes a charm of negative one.

Looking at our omega baryon, we can say then that this charm quark contributes a charm of positive one, so does this one here, and so does the third one. The total charm for the omega baryon will be the charm of each of these quarks combined, added together. One plus one plus one is three. So, that is the charm of this omega baryon.

Now, let’s look at the second part of our question, which asks about the relative electric charge of the particle. To figure this out, once again we’ll use the properties of the charm quark. This quark, which we color in red because it has a positive electric charge, has a relative electric charge of positive two-thirds times e, where e is the charge of a single proton. Since each one of the charm quarks in our particle has this same relative charge and note that here we’ve left off the e as we sometimes do, then we can say that the omega baryon’s relative electric charge equals the sum of these individual charges. Positive two-thirds plus two-thirds plus two-thirds is six-thirds, or two. So, this is the relative electric charge of this omega baryon.

Let’s look now at one last example exercise.

The following equation shows a D meson decaying into a kaon and two pions. What is the total charm before this interaction takes place? What is the total charm after this interaction takes place?

The equation we see shows us a D meson, made up of a charm quark and an up antiquark, decaying into a positively charged kaon, made of an up quark and a strange antiquark, a positively charged pion, made of an up quark and a down antiquark, and then lastly a neutral pion, made of an up quark and an up antiquark. It’s important to know what quarks make up each of these particles because that will help us answer these questions about the total charm in the interaction.

We can recall that this property called charm is determined by the number of charm quarks and charm antiquarks a particle may possess. Every charm quark contributes a charm of positive one, while every charm antiquark contributes a charm of negative one. Any quarks that are not of this type do not contribute to the charm of the particle overall.

Knowing this, we can figure out the answer to the first part of our question by computing the charm of our D meson. This is the only particle that exists before the interaction. And we see that it’s made up of one charm quark, that contributes a charm of positive one to the meson, and one up antiquark. This particle makes no contribution to the overall charm. The overall charm of the D Meson, then, is positive one. This is the total charm in this equation before the interaction takes place.

The second part of our question asks about the total charm after the interaction has taken place. At this point, the D meson has decayed into the kaon and the two pions. So now, we want to calculate the total charm for these three particles combined. We’ll do this by adding together the charm of each individual particle. First, we consider the kaon. The quarks that make it up are the up quark and the strange antiquark. Neither of these impacts the charm of the particle overall, which means that its charm is zero.

Considering next our positive pion, we see this is made of an up quark and a down antiquark. These also have no impact on charm. So therefore, the charm of this particle is zero too, and so is the charm of our neutral pion because this also is not made up of any charm quarks or charm antiquarks. The way we figure out the total charm after the interaction has taken place is by adding together the charm of what we could call the products. Zero plus zero plus zero is zero. So, that is the total charm after the interaction. And note that in this interaction, charm is not conserved. It started out as one and ended up as zero.

Let’s summarize now what we’ve learned about charm. In this lesson, we saw that charm is a property of subatomic particles. It’s determined by the number of charm quarks and antiquarks these particles may possess. The rule for calculating charm is that for every charm quark possessed by a particle that contributes a charm of positive one, while every charm antiquark contributes a charm of negative one. We saw further that the total charm of a composite particle equals the sum of the charms of the particles that make it up. For example, a baryon made of three charm quarks would have an overall charm of positive three. We saw further that any particle with no charm quarks or antiquarks has an overall charm of zero. This includes all leptons. Lastly, we saw that charm is conserved under strong and electromagnetic interactions but not under weak interactions. This is a summary of charm.