### 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.