Video: Gluons

In this video, we will learn the basic properties of gluons and how they interact with quarks.

15:42

Video Transcript

In this lesson, we’re going to learn about gluons, particles from the standard model of particle physics that play a key role in the interactions between quarks.

In particular, gluons mediate the strong interaction, which affects a property of quarks and gluons known as color charge. Okay then, let’s unpack this statement. Color charge is a property of quarks and, it turns out, also gluons that in some ways is very similar to the electric charge, hence, the name charge, but in some keyways is very, very different. Electric charge comes in a pair of two opposite values; we usually call them positive and negative. Color charge also comes in pairs of opposite values, but instead of just one such pair, there are actually three. Inspired by the three primary colors, we call them red and antired or cyan, green and antigreen or magenta, and blue and antiblue or yellow.

To make a notation easier to write and use, we’ll use a colored letter to represent each color charge — r for red, g for green, and b for blue — and the same letter but with a bar over it to represent the corresponding anticolor charge. It’s important to stress that these colors have nothing to do with the phenomenon of color that we experience in our everyday lives. The color that we see with our eyes is an electromagnetic phenomenon, while color charge is related to the strong force.

Like electric charge, though, color charge is conserved. That is the total color before an interaction must be the same as the total color after an interaction. The main difference between electric charge and color charge is that the electric charge of a particle is fixed, but the color charge is not. Think of any particle in the standard model, like, say, an electron. Every electron has the same electric charge.

The same is not true for color charge. Every quark has a color charge. So say a down quark could have a color charge of red, green, or blue, but no matter the particular value of its color charge, it is still a down quark. The only restriction is that quarks have the regular colors of color charge, and antiquarks have the anticolors. So, an antidown quark could have an antired color charge, but not a green color charge.

The fact that color charge is not a fixed quantity for a particular kind of quark is actually incredibly important because the strong force is, in a sense, just the constant fluctuation of a particle’s color charge. And as it turns out, gluons are the mediators of that force. Here again, we can draw an analogy to electromagnetism, where we’ll find many similarities and also some key differences.

Like the photon which mediates the electromagnetic force, the gluon is a boson. Also, like the photon, the gluon has no electric charge and also no mass, at least in theory. In practice, it’s so difficult to measure gluons that we don’t know for sure that their mass is zero. Nevertheless, the experimental limits on their maximum possible mass are very close to zero. And the theory that suggests that their mass is exactly zero seems to be quite sound. The fundamental difference between gluons and photons is that photons have no color charge, but gluons do have color charge. The color charge of gluons is the property that completely changes how physics treats the strong force compared to the electromagnetic force.

Because the photon has no electric charge, even though it mediates the electromagnetic force between two charged particles, it itself does not experience that force. On the other hand, since gluons do have color charge, not only do they mediate the strong force between quarks, they themselves experience the strong force. This fact is actually what gives the strong force most of its unusual properties. Strange as it may seem, though, the fact that gluons carry color charge is totally consistent with the properties of color charge itself. Because quark color charge can change, the only way that color charge can be conserved is if the particles mediating that change themselves have color charge.

We know that quarks can have red, green, or blue color charge. To understand what kind of color charge gluons can have, let’s consider an example of an up and a down quark changing colors. Here’s a Feynman diagram representing the interaction. Let’s make sure we know what we’re looking at. We have axes of time and position, and lines on the diagram represent somewhat abstracted versions of particle trajectories.

Solid lines with arrows represent quarks. Each line is labeled with the type of quark and also colored according to the quark’s color charge. So, this line is an up quark with a blue color charge, and this line is a down quark with a red color charge. This curly line, labeled with the letter g, is called a cycloid. And g is the label of the gluon whose color we’re trying to determine. Like straight lines with arrows for quarks and leptons and wavy lines for photons, the cycloid is the special line shape used in Feynman diagrams to represent gluons.

Let’s use the fact that color charge is conserved to deduce the color of the gluon from this vertex. The only color charge entering the vertex is red from the up quark. Leaving the vertex, we have blue from the up quark and the unknown color of the gluon. Let’s now conserve color charge exactly like we would conserve electric charge.

The only color entering the interaction is red, so one of the colors leaving the interaction must also be red. Since blue is not red, the gluon must have red color charge. Now, we have red entering the interaction and red leaving the interaction. But we also have blue leaving the interaction. Since there’s no blue entering the interaction, this blue leaving the interaction must be balanced by antiblue. So, in order to conserve color charge, the gluon must actually have two color charges, red and antiblue.

The possibility of a fundamental particle to effectively carry two different color charges is yet another distinction between color charge and electric charge. We represent the gluon colors on the Feynman diagram by writing the appropriate symbols next to the letter g. Using the subscript r for red and b with the bar for antiblue, this whole symbol tells us that we’re dealing with a red-antiblue gluon. Let’s double-check that this gluon conserves color charge at the vertex, where a down quark with a blue color charge becomes a down quark with a red color charge.

Going into the vertex, we have blue and red-antiblue. Leaving the vertex, we just have red. The combination blue plus antiblue results in no color charge, also known as colorless. This leaves red as the only remaining color going into the interaction. Red is also the only color leaving the interaction. And indeed, color charge is conserved. So at least as far as conservation of color charge, red-antiblue is the correct choice for gluon color in this interaction.

There are two important points that we can learn from this diagram. First, although both quarks change color, they don’t change type. That is, an up quark stays an up quark and a down quark stays a down quark. This is characteristic of the strong force mediated by gluons. Quark color changes, but quark type doesn’t. Interactions where quark type changes are examples of the weak force.

Second, in order to make this interaction work, the gluon must have two color charges, a color and an anticolor. This is, in fact, generally true. Gluons always behave in interactions like a particle with a color-anticolor pair of color charges. In our particular example, these color charges worked out to red-antiblue. But in a different example, they might work out to blue-antigreen, or any such combination.

The reason we’ve specified a gluon’s color charge by how it interacts rather than its actual intrinsic color is because of the following physical fact. Exactly eight types of gluon exist, which are distinguished by having different color charges. However, if we assume that the color charge of a gluon is exactly one color and one anticolor, then we have three choices for color and three choices for anticolor, which should give nine types of gluon. So, how can there be only eight types of gluon if we would predict nine? Well, it turns out that the true color structure of a gluon is more complicated than simply a single color and a single anticolor. No matter how we manipulate the structure mathematically, we will always find exactly eight gluons with color charge and exactly one particle that is colorless.

This colorless particle doesn’t participate in the strong interaction because the strong interaction only affects particles with color charge. This is why we specify the gluons always interact as if they have a single color charge and a single anticolor charge. Even though the underlying structure of their color charges may be more complicated, gluons always behave in a particular interaction, as if they have exactly one color charge and one anticolor charge.

All right, now that we’ve learned some basic facts about the gluon, let’s work through some examples.

The Feynman diagram shows a delta baryon, down, down, down, decaying to a neutron, up, down, down, and a meson. What is the particle X?

The particle X that we’re looking for is down here in the bottom-right corner of the diagram. Before we go about finding its identity, though, let’s make sure we understand what this diagram is showing. On the left-hand side of our diagram corresponding to the initial configuration, we have three down quarks close together. This is the delta baryon. On the right-hand side of the diagram, which corresponds to the final configuration, we have two down quarks and one up quark close together, which is the neutron, and an anti-up quark together with the mystery particle X, which must form the meson.

In the interior of the diagram, two of the down quarks don’t undergo any interactions at all. The last down quark, however, reaches a vertex where it becomes a gluon represented by a cycloid and the mystery particle X. This gluon then reaches another vertex where it spontaneously decays into an up quark, which become as part of the neutron, and an anti-up quark, which become as part of the meson.

All right, now that we’ve understood what’s being shown in this diagram, let’s start gathering what we know about the particle X. Firstly, just by looking at the diagram, we know that X is a particle, not an antiparticle, since the line representing X has an arrow that points forward in time. Just for contrast, the line representing the anti-up quark has an arrow that points backwards in time because an anti-up quark is an antiparticle. The next piece of information we can gather about X is whether it is a lepton, a quark, or a boson.

From the diagram, we know that X is part of a meson. And we can recall that a meson is a composite particle made up of one quark and one antiquark. Since the anti-up is the antiquark of the meson, X must be the quark. Even without knowing that the anti-up X pair forms a meson, we could’ve still determined that X is a quark by conserving baryon number. At this vertex here, a down quark becomes a gluon and the mystery particle. Since the gluon is a boson, it has a baryon number of zero. Therefore, to conserve the baryon number of the down quark, X must also be a quark. All that’s left now is to determine which quark.

The only other clue we have as to the identity of X is that it participates in the interaction at this vertex where we conserved the baryon number. Since the particles at this vertex are two quarks and one gluon and the gluon is the boson that mediates the strong force, this vertex must represent a strong interaction. Recall that the strong interaction affects particles with color charge like quarks and gluons and can only change the color charge of quarks, not their type. Interactions that change quark type are weak interactions and are mediated by W and Z bosons.

So, although we don’t know the color charges of the down quark entering the vertex or the gluon and the particle X leaving the vertex, we know that whatever type of quark enters the vertex must be the type of quark that leaves the vertex. Since the quark entering the vertex is a down quark, the quark leaving the vertex, namely, the particle X, must also be a down quark.

It’s interesting to note that we arrived at this answer that X is a down quark not by knowing what the strong interaction did do to the down quark, but by knowing what it didn’t do. That is to say, by knowing that the only thing that the strong interaction could have done to this down quark is change its color charge, we were able to deduce that it did not change the quark type.

Great, let’s see another example.

The Feynman diagram shows two up quarks exchanging a gluon. What is the color charge of the gluon?

Before we go anywhere with answering this question, since it’s a question about color charge, let’s add some color to our diagram. We’ve now colored the up quark symbols and their corresponding lines on the diagram so that their color matches the color in the parentheses. This isn’t actually a necessary step for solving the problem, but it will help us visualize what we’re working with. Since we’re dealing with color charge in this question, let’s recall some key facts about color charge.

Color charge is a property of quarks and gluons, and it comes in three pairs of values. We abstractly call them red and antired, green and antigreen, and blue and antiblue. Just like a positive electric charge is the opposite value of a negative electric charge, an anticolor charge is the opposite value of the corresponding color charge. For example, antiblue is the opposite value of blue. Also like electric charge, color charge is a conserved quantity. That is, the total color of all the particles entering an interaction must be the same as the total color of all the particles leaving an interaction.

These few facts about color charge are actually all that we need to answer this question. There is, however, one useful fact about the color charge of gluons that will help us make sure that our answer is on the right track. When gluons participate in interactions, they always do so with two color charges, one color — red, green, or blue — and one anticolor — antired, antigreen, or antiblue. With all this in hand, let’s conserve color charge in our Feynman diagram, starting with the top vertex.

Using our notation for representing color charge, we can write that green color charge becomes blue color charge plus the unknown color charges of the gluon. Since blue appears in the final configuration but not in the initial configuration, it must be balanced by antiblue in the color of the gluon. Furthermore, since green is the only color appearing in the initial configuration, it must also appear in the final configuration.

Since the final color of the up quark is blue, not green, this green must be accounted for in the color of the gluon as well. So, a gluon with color charge green-antiblue will conserve color charge at this vertex. Let’s double-check that this gluon also conserves color charge at the second vertex where an up quark with blue color charge becomes an up quark with green color charge.

Going into the vertex, we have blue from the quark and green-antiblue from the gluon. Going out of the vertex, we only have green from the quark. Adding up the total color of the particles entering the interaction, blue from the up quark is exactly cancelled by antiblue from the gluon, which leaves a net color of green, also from the gluon. The total color leaving the interaction is just the single green charge of the up quark. Because the total color both before and after this interaction is green, we see that a green-antiblue gluon does indeed ensure that color charge is conserved at this vertex. So, by conserving color charge at each vertex, we’ve both determined and confirmed that the color charge of this gluon is green-antiblue.

All right, now that we’ve worked through a few examples, let’s review what we’ve learned about gluons. In this lesson, we learned that gluons are the bosons that mediate the strong force, which is the force responsible for quarks constantly changing their color charge. We also learned that gluons are similar to photons, which are the bosons that mediate the electromagnetic interaction, and that gluons have no electric charge and also, at least in theory, have no mass.

In practice, experiments have not found a precise value for this mass due to the difficulty in measuring gluons. Even though a precise value is not known, available experimental data does agree with a mass of zero. Unlike photons, though, which don’t carry electric charge even though they mediate the electromagnetic force, gluons which mediate the strong force do carry color charge. In particular, when gluons interact, they can always be treated as carrying two color charges, one of which is a color and one of which is an anticolor. This color-anticolor pair is what allows the strong force to cause quark color charge to change. Furthermore, since gluons themselves have color charge, they not only mediate but also participate in strong force interactions.

The last property of gluons that we learned is that they come in eight types determined by their color charges. We also discussed briefly how each gluon color type does not necessarily correspond directly to a single choice of a color and anticolor. This explains how there can be only eight gluon color types, even though there are nine possible combinations of a single color and a single anticolor.

Lastly, we learned that a special curly line called a cycloid is used to represent gluons in Feynman diagrams and that strong interactions mediated by gluons can only change a particle’s color charge, but not the particle’s type.

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