### Video Transcript

In this video, we’re talking about
strangeness. In the world of high-energy
physics, this term has a very specific meaning. We’re going to learn what that
meaning is. And we’ll also find out how to
calculate the strangeness of a given particle.

When we first hear this term,
strangeness, we might think of the six different types of quark and recall that
strange is one of those types. And indeed, the strangeness of a
given particle does have to do with how many strange quarks it possesses. And yet, historically, strangeness
was a concept in physics even before quarks had been discovered. As researchers studied high-energy
collisions amongst particles that were very unusual, that is, strange, they noticed
that in some of these interactions, there seemed to be a quantity that was
conserved, much like energy or charge is conserved. This quantity was called the
strangeness of a nuclear interaction, and it referred to the collective strangeness
of the particles involved.

By way of example, consider this
interaction of subatomic particles. This first particle here, the one
with a K and a zero in its superscript, is called a kaon. Then we have a proton and then a
charged kaon, that’s where the positive sign in the superscript comes from, and then
lastly a neutron. In this overall interaction then,
we have a neutral kaon combining with a proton to yield a charged kaon and a
neutron.

Now, earlier, we mentioned that
this term strangeness was originally thought to be a conserved quantity like, say,
electric charge. If we looked at this nuclear
interaction from the perspective of electric charge, we would see that the neutral
kaon has a net charge of zero. The proton has a relative charge of
positive one. Then, on the other side, our
charged kaon has a charge of positive one, and a neutron has a charge of zero. Since the total charge on each side
of this equation is the same, we say that for this interaction, it’s conserved.

Just as we can analyze nuclear
equations for their relative charge, we can do the same thing for their
strangeness. To do this though, we’ll need to be
looking not at the particles themselves, but at the quarks that make them up. Now, if we look at the quarks that
make up a neutral kaon, those are the down quark and the strange antiquark. Recall we said earlier that
strangeness is connected with strange quarks. That’s true, and here’s how it
works.

If we have one strange quark by
itself, then the strangeness of that strange quark, we’ll represent it with a
capital 𝑆, is equal to negative one. And then if we have a strange
antiquark, symbolized by an 𝑆 with a bar over top of it, the strangeness of that
particle is positive one. The fact that the strangeness of a
strange quark is equal to negative one while that of a strange antiquark is positive
one comes down to historical reasons. For our purposes, the important
thing is to remember these relations.

Any time we see a strange quark in
a particle, we know that contributes a strangeness of negative one, while every
strange antiquark contributes a strangeness of positive one. And this brings us back to the
quarks that make up our neutral kaon: a down quark and a strange antiquark. Of the six quark types, the only
one that contributes to the strangeness of a particle is the strange quark and its
antiparticle, which means that this down quark doesn’t contribute anything to the
strangeness of our neutral kaon. But the strange antiquark, on the
other hand, does. We see, according to our rule, that
it gives a strangeness of positive one to this particle. So the strangeness of a neutral
kaon is positive one.

And next, to figure out the
strangeness of our proton, let’s look at the quarks that make up this particle. A proton is made up of two up
quarks and one down quark. None of these contribute anything
to the strangeness of a proton. So overall, its strangeness is
zero. Then, if we go to the other side of
our interaction, to our charged kaon, this is made of an up quark and a strange
antiquark, where, as always, the only contributor to the strangeness of the particle
comes either from a strange quark or a strange antiquark.

Our rule tells us that every
strange antiquark contributes positive one, which means that the overall strangeness
of this charged kaon is positive one. And then, for our neutron, this is
made of an up quark, a down quark, and another down quark, none of which contribute
to the strangeness of the particle. So its overall strangeness is
zero.

Looking at this interaction as an
equation, we see that the strangeness on the left adds up to one and the total on
the right is the same. In this interaction then,
strangeness is conserved just like electric charge. But there’s an important difference
between the two. While electric charge, as far as we
know, is always conserved in nuclear interactions, strangeness is not. When it is, as it is in this case,
that tells us something about the interaction taking place.

Recall that the four fundamental
forces are called the strong force, the electromagnetic force, the weak force, and
gravity. Whenever strangeness is conserved,
that means the force involved in an interaction is either the strong force or the
electromagnetic force. So that must be the case here, that
one of those two forces is governing this reaction. It turns out though that if it’s
the weak force that dominates in an interaction, then strangeness need not be
conserved.

Now, just looking at a nuclear
equation, we couldn’t tell offhand which of the forces is responsible. The way we figure that out is by
calculating the strangeness on both sides, seeing if it’s conserved, and then
working back. As we saw, the only way for a
particle to have a strangeness that is not equal to zero is if it’s made up of at
least one strange or one antistrange quark. For a given particle, for every
strange quark it possesses, we add a strangeness of negative one to the particle
overall. And then, for every strange
antiquark, we add a strangeness of positive one. When we calculate the strangeness
of a given particle then, if we know that it doesn’t have any strange quarks or
strange antiquarks, we can say right away that its strangeness is zero. That was what happened in the case
of our proton and our neutron.

Knowing all this about strangeness,
let’s get some practice now through an example.

A 𝛯 baryon is a baryon with the
composition uss. What is the strangeness of the 𝛯
baryon?

Okay, so here we’re being told
about this particle called a 𝛯 baryon. And we’re told what it’s composed
of, in particular, the types of quarks that make it up. We’re told that if we take an up
quark and then join it with a strange quark and another strange quark, then what we
have is this particle called a 𝛯 baryon and symbolized using the Greek letter
𝛯. As a side note, this superscript
zero indicates the overall relative charge of this baryon.

An up quark, we can recall, has a
relative charge of positive two-thirds times the charge of a proton, while a strange
quark has a relative charge of negative one-third e. If we add together all the relative
charges of these quarks, we get a result of zero, the relative charge of the
particle overall. But of course what we want to know
is the strangeness of this particle, and we’ll calculate that in a different
way.

Strangeness is a property of a
particle that comes down to how many strange quarks and strange antiquarks it
possesses. For every strange quark a particle
possesses, we add a strangeness of negative one to it. And then for every strange
antiquark, we add a strangeness of positive one. And then the overall strangeness of
the particle is equal to the sum of these individual strangenesses.

Let’s call the strangeness of our
𝛯 baryon capital 𝑆. And before we start counting any of
the quarks in this particle, let’s say our strangeness starts out at zero. First, we look at the up quark. And this, like all quarks other
than the strange quark, contributes nothing to strangeness. So the strangeness of our particle
is still zero at this point. Then we move on to this first
strange quark here. According to our rule, every
strange quark contributes a strangeness of negative one. So at this point, the strangeness
of our 𝛯 baryon is no longer zero, but we have negative one. And then we move on to the second
strange quark here. Just like the first one, this also
contributes a strangeness of negative one to the particle overall, so that once all
of our quarks are accounted for, we have a total strangeness for this particle of
negative two. And that’s our answer. The strangeness of a 𝛯 baryon with
zero net charge is negative two.

Let’s now look at another example
exercise.

A phi meson is a particle that is
made up of a strange quark and a strange antiquark. What is the strangeness of a phi
meson?

Let’s say we represent this
particle using the Greek letter Φ. Now, because this particle is a
meson, we can recall that that means it’s made up of one quark and one
antiquark. And indeed we’re told that this
particle is made up of a strange quark and a strange antiquark. We then want to figure out what is
the strangeness of a phi meson.

Strangeness, we can recall, is a
property of particles as well as nuclear interactions. The strangeness of an interaction
comes from the number of strange quarks and strange antiquarks involved. The rule for determining
strangeness is, for every strange quark involved, a strangeness of negative one is
contributed. And then every strange antiquark
has a strangeness of positive one.

Now, the fact that the strangeness
of a strange quark is negative one and that of a strange antiquark is positive one
might seem a little strange, get it? But the reason for this comes down
to the historical fact that the concept of strangeness preceded the discovery of
quarks.

Anyway, we can now use these rules
to figure out the strangeness of our phi meson. Before we count up any of the
quarks involved, let’s say that our particle has an overall strangeness of zero. We can consider this our starting
value. And then as we take into account
this strange quark, our rule tells us that that contributes a strangeness of
negative one. At this point then, that’s the
strangeness of our particle overall. But then we consider the
contribution of our strange antiquark. And going back to our rule, this
contributes a strangeness of positive one. So our strangeness overall is
negative one plus one, or simply zero. And this is the strangeness of our
phi meson. The strangeness of the strange
quark and that of the strange antiquark canceled one another out.

Let’s look now at one last example
exercise.

The following equation shows a Xi
baryon decaying into a lambda baryon and a pion, which is an interaction that does
not conserve strangeness. What is the total strangeness
before the interaction takes place? What is the total strangeness after
the interaction takes place?

Looking at our equation, we see
this particle here, called a Xi baryon, decaying into a lambda baryon and a
pion. Along with the symbol for each of
these particles, in parentheses, we’re told what quarks make up each one. So, for example, for our pion, this
is made up of an up antiquark and a down quark.

Our question is focused on the
strangeness of this interaction. And we can recall that this has to
do with how many strange quarks and strange antiquarks are present. Specifically, every strange quark
in a particle has a strangeness of negative one, while every strange antiquark has a
strangeness of positive one. This means, for example, that if we
had a strange quark all by itself, then the strangeness of that particle would be
negative one.

The first part of our question asks
about the total strangeness before the interaction takes place. In other words, what is the
strangeness of the Xi baryon before it decays into the lambda baryon and the
pion? We see that this particle is made
up of a down quark and two strange quarks. The down quark doesn’t contribute
anything to strangeness. Only strange quarks and strange
antiquarks can. But each one of the strange quarks,
according to our rule, will contribute negative one to the overall strangeness of
the particle. So if we call 𝑆 sub b the total
strangeness before our interaction takes place, that’s equal to zero, that’s the
contribution of the down quark in the Xi baryon, minus one minus one. Those are the contributions of the
two strange quarks. So that equals negative two. And that’s our answer to the first
part of our question.

Part two asks us, what is the total
strangeness after the interaction takes place? Now, if strangeness was conserved
in this equation, then our answer here would be the same as our answer earlier. But our problem statement tells us
that, in this case, strangeness is not conserved. So let’s take a look at the product
side of this interaction.

First, we have our lambda
baryon. And we see this is made of an up
quark, a down quark, and a strange quark. Both the up and the down quark
don’t contribute anything to the strangeness of this particle overall, while the
strange quark, according to our rule, contributes a strangeness of negative one. We can say then that the overall
strangeness of our lambda baryon is negative one.

And next, we look at the pion,
which we see is made up of an up antiquark and a down quark. Since neither of these is a strange
quark or a strange antiquark, they contribute nothing to the strangeness of the
pion. And so we can say that the
strangeness of the pion overall is zero. This means that the total
strangeness of this interaction after the interaction takes place is negative one
plus zero or just negative one. And we see now that indeed
strangeness is not conserved in this interaction. Before the interaction, it was
negative two. And after, it’s negative one.

Let’s now summarize what we’ve
learned about strangeness. In this lesson, we learned that
strangeness is a property of particles that depends on how many strange quarks and
antiquarks they possess. Every strange quark possessed by a
particle contributes a strangeness of negative one, while every strange antiquark
contributes a strangeness of positive one. This means that any particle that
has neither a strange quark nor a strange antiquark has a strangeness of zero. And lastly, we saw that when
particles interact according to the strong and electromagnetic forces, then the
overall strangeness is conserved, while in weak interactions, that strangeness is
not conserved. This is a summary of
strangeness.