Video: Hadrons

In this video, we will learn how to identify which classes of hadron a given particle belongs to and what the properties of given hadrons are.

14:25

Video Transcript

In this video, we’re talking about hadrons. As we’ll see, hadrons are particles that are made up of even smaller particles called quarks. In this lesson, we’ll learn the names for different types of hadrons as well as the rules for forming them. We can get started by defining a hadron as a subatomic particle that’s made of two or more quarks. Regarding quarks, we can recall that there are six distinct types, up, down; charm, strange; and top, bottom, and that each type has its own corresponding antiparticle or antiquark.

Each quark and antiquark has its own relative electric charge. And if we focus on the top row in our grid, we can say that the quarks in this row, the up, charm, and top quarks, all have a relative electric charge of positive two-thirds e, where e is the charge of a single proton. The corresponding antiquarks, on the other hand, have a relative charge of negative two-thirds e. Similarly, on the bottom row of our grid, the three quarks have a relative charge of negative one-third the charge of a proton, while the antiquarks have that same charge magnitude but the opposite sign. We go into all this detail about quarks because these are the building blocks, we could say, of hadrons.

Every hadron is made up of some collection of quarks and/or antiquarks. There are many possible ways of combining quarks and antiquarks to form hadrons. However, not all combinations are allowed. We can extend our definition of hadron to be a subatomic particle made up of two or more quarks, such that the total relative charge of the particle is an integer. That is, however we add quarks and antiquarks together to form a hadron, the total charge of that particle must be a whole number. It can be positive or negative or even zero, but it needs to be an integer.

To give an example of this, say that we take an up quark, which we know has a relative electric charge of positive two-thirds e, and we’ll just leave off the e for now, and that we combine this with a down antiquark. This, we know, has a relative electric charge of positive one-third. So if we add together these two charges, we get a result of one. That’s the overall relative electric charge of this combination. Since this is an integer, that means that this combination of particles is allowed in forming a hadron. In other words, this particle is a hadron. And in fact, it’s called a pion; the symbol for this is 𝜋 with a plus sign superscript.

But then say we go back to having just an up quark. And now, instead of adding it with a down antiquark, we propose to add to it a top quark. From our grid, showing the relative charge of quarks, we know that each of these quarks has a charge of positive two-thirds. So if we add them together, we get this result of four-thirds. Since this is not a whole number, it means that just combining these two quarks by themselves is not an allowed combination in forming a hadron. Even under this restriction that the relative charge of a hadron needs to have an integer value, there are still many ways of combining quarks and antiquarks to form them, so many that if we consider hadrons as a class of particle, this class has been divided up into smaller groups.

One type of hadron is called a meson. These are hadrons that are made up of two quarks, in particular one quark and one antiquark. After mesons come a class of particle called baryons. These are hadrons that are made up of exactly three quarks. And then it’s possible to make hadrons from four or five or six or even more quarks. But these are so rare or yet to be discovered that they don’t yet have commonly used names. Our focus will be on mesons, which, as we said, are made of two quarks, and baryons, which are made of three. And then it turns out that baryons themselves can be further subdivided. One sort of baryon is called a hyperon. Like any baryon, a hyperon is made up of exactly three quarks. But the hyperon has the special condition that at least one of those quarks is the strange quark, while at the same time it has no charm, top, or bottom quarks in its composition.

One way we can be helped to remember this is that if we think of hyperon as a bit of a strange name, we can be reminded that it has at least one strange quark. And then of the four least common quark types, charm, strange, top, and bottom, it has only strange and no charm, top, or bottom. As an example of a hyperon, we could bring together one up, one down, and one strange quark. Note that the relative charge of one up quark is positive two-thirds, that of a down quark is negative one-third, and it’s the same for a strange quark, giving a total relative charge of zero. Zero is an integer, so this is an allowed combination of quarks to make up a hadron.

This particular hyperon has a name. It’s called a lambda baryon. It’s represented by the Greek letter capital 𝛬. And notice the zero in the superscript indicating its relative charge. So that’s an example of a hyperon. But what about a baryon that is not a hyperon? This would be any combination of three quarks, where none of those quarks is a strange quark. And the overall relative charge is a whole number. If we take an up quark, an up quark, and a down quark and bring them all together, the relative electric charge of each up quark is positive two-thirds and that of the down quark is negative one-third. So the total relative charge is positive one. And actually, by bringing these three quarks together, what we’ve created is a proton.

A proton is a hadron; specifically, it’s a baryon. And we see that, just as we would expect, it has an overall relative charge of positive one. By the way, if we were to take one of these two up quarks and then replace it with a down quark, then in that case instead of a proton, we would have a neutron. And notice, once again, just as we would expect, if we now add up the total charge of this particle, we find that it is zero. It’s an electrically neutral particle. So both protons and neutrons are baryons that are not hyperons. Now let’s look at an example of a meson particle.

As we said, these are particles that consist of two quarks and in particular one quark and one antiquark. An example of a meson includes a particle that we looked at earlier, the pion. As we saw, this consists of one up quark and one down antiquark. And when we added together the relative charge of each of these two particles, we found they added up to positive one. Interestingly, because of the way that the relative charges for our quarks and our antiquarks are assigned, any meson will always have a relative charge of either plus one, zero, or negative one. Those are the only three options for valid mesons. Now that we know what hadrons are as well as some subtypes of this class of particle, let’s get some practice with these ideas through an example.

Which of the following particles are hadrons? mu neutrino, lambda baryon, charm quark, top antiquark, pion, proton, electron.

To figure out which of these particles are and are not hadrons, let’s first recall what this term means. A hadron is a composite particle made up of two or more quarks with a total relative charge equal to some integer value. To understand hadrons then, we need to understand quarks and their antiparticles, antiquarks. The six types of quark are up and down, charm and strange, and top and bottom, where the three quarks in the top row of this grid have a relative electric charge of positive two-thirds times the charge of a single proton, while those in the bottom row have a relative charge of negative one-third e, while each corresponding antiquark has a charge of the same magnitude, but the opposite sign.

Hadrons then are made up of these six types of quarks and their antiparticles. And so, the first test we can apply to these particles to see if they’re hadrons is to determine whether they’re made up of two or more quarks or not. Starting at the top of our list, our first particle is called a mu neutrino. This is a fundamental particle. That is, it’s not made up of any smaller particles as far as we know, and, therefore, it doesn’t meet the condition of being made up of two or more quarks, as all hadrons are. This shows us that a mu neutrino is not a hadron, so we’ll cross off that option.

Next, we come to the lambda baryon. This is a particle that is made of quarks. And in fact, the three quarks that it’s comprised of are given to us. If we bring together an up, a down, and a strange quark, then we have what’s called a lambda baryon. So this particle is made of two or more quarks. And now we just need to know whether its total relative charge is equal to an integer. To figure that out, we’ll add together the relative electric charge of each of these three quarks. Based on our grid of quarks and antiquarks, an up quark has a relative electric charge of positive two-thirds, and we’ll leave off the e.

A down quark, on the other hand, has a relative electric charge of negative one-third, and so, we see, does a strange quark. If we add all these up, we get a result of zero. Now zero is an integer value, and so that means it satisfies the second condition of a hadron. Therefore, a lambda baryon is a hadron, and we’ll box in this particle as part of our answer. Moving on, we come to the charm quark. Just as a side note, if we saw this without any context, we might think that this c refers to the speed of light in vacuum. The only way we really know that this refers to a charm quark is because we’re told that it is a particle. And therefore, we identify it with this particular quark type.

As we’ve seen, a hadron is a composite particle made up of two or more quarks. So one quark all by itself can never make a hadron. The charm quark, then, is not a hadron. Moving down to the top antiquark, for the same reason, this also is not a hadron. A hadron needs to have at least two quarks. This brings us to the pion which we’re shown is comprised of an up quark and a down antiquark. If we draw that out, it looks like this. And so this particle is made up of two or more quarks. In particular, it’s made of two. So once again, we need to test whether its total relative charge is equal to an integer. The relative charge of an up quark is positive two-thirds and that of a down antiquark we see is positive one-third. This adds up to one, which is an integer, which means that this particle, called a pion, is indeed a hadron.

We’ll box that particle then and move on to consider the proton. A proton is made up of two up quarks and one down quark. That would look like this. And once again, we’ll look at the total charge for this particle. Each of the up quarks contributes a relative charge of positive two-thirds, while the down quark, negative one-third. And this adds up to three-thirds or simply one. Just like we would expect, the total charge for this proton is positive one. And since that’s an integer, it means that a proton is a hadron.

The last particle we’re to consider is an electron. Like a mu neutrino, an electron is an elementary or fundamental particle. It’s not made of anything smaller than itself, so it’s not made up of two or more quarks. This tells us that an electron is not a hadron. So of this list of particles, the lambda baryon, the pion, and the proton are hadrons.

Let’s look at one more example exercise.

Which of the particles shown in the diagram are mesons? The quarks shown in the diagram are colored according to their electric charge.

Okay, we see these six particles marked (a), (b) (c), (d), (e), and (f). And we want to figure out which of them are mesons. We’re told that the quark shown in this diagram are colored according to their electric charge. Positively charged quarks, like the up quarks in particle (a), are colored red and negatively charged quarks, like the down quark here, are colored blue. Now mesons are a class of particle that are defined by two conditions. First, they’re made up of one quark and one antiquark. And second, the total relative charge of a meson is an integer value. Considering this first condition that mesons are made of one quark and one antiquark, we see right away that three of these particles don’t meet that condition.

Particles (a), (d), and (f) are all made of three quarks and therefore can’t be mesons, leaving us with particles (b), (c), and (e). Looking at these three, we see that each one is indeed made up of one quark and one antiquark. So all that remains to be seen is if each one has a total relative charge of an integer value. Looking first at particle (b), we can recall that an up quark has a relative electric charge of positive two-thirds, where this is positive two-thirds times the charge of a single proton, while a down antiquark has a relative electric charge of positive one-third. Two-thirds plus one-third equals one, which is an integer. So particle (b) satisfies both of our conditions and therefore is a meson.

Considering next particle (c), we know that a strange quark has a relative electric charge of negative one-third times the charge of a proton, while an up antiquark has a relative charge of negative two-thirds. Adding these two charges together, we find a result of negative one, which also is an integer. So particle (c) is a meson as well. The charm quark in particle (e) has a relative charge of positive two-thirds and the down antiquark has a relative charge of positive one-third. Combining these charges gives an overall charge of one. So this particle too is a meson. In this diagram then, particles (b), (c), and (e) are all mesons.

Let’s summarize now what we’ve learned about hadrons. In this lesson, we saw that a hadron is a composite particle made up of two or more quarks having an integer-value total relative charge. We learn further that the class of particles called hadrons are divided up into various types. Mesons we saw are hadrons that are made up of exactly two quarks, in particular, one quark and one antiquark. Baryons are hadrons that are made of exactly three quarks. And baryons themselves can be further divided into groups of particles. One of these groups is called hyperons.

A hyperon we saw is a baryon. That is, it’s made of exactly three quarks. But for a hyperon, at least one of those quarks is a strange quark. And none of them are a charm, top, or bottom quark. Lastly, through several examples, we saw that any hadron’s total charge is equal to the sum of the charges of the quarks that make up that hadron. This is a summary of hadrons.

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