Lesson Video: Color Charge Physics

In this video, we will learn how to determine which combinations of color charge quarks must have in order for them to form hadrons.


Video Transcript

Our topic in this video is color charge. We’re going to learn that this sort of charge is a property of particles called quarks. And we’ll also learn the rules that govern what kinds of color charge quarks can have when they’re grouped together. Now, just the idea that there is a kind of charge called color charge might seem strange. So, let’s start out by recalling what we know about electric charge. Electric charge comes in two varieties, positive and negative. And when two objects have a net electric charge, that charge affects how they interact with one another.

When we talk about color charge, we’re effectively building off of this idea. Except now, instead of two kinds of charge, there are three, and those charges are represented by colors. One kind is red, another kind is blue, and the third is green. One important thing to realize is that if a particle does have, say, a blue-colored charge, that doesn’t mean the particle is actually blue in color, but rather that it has that sort of charge. And we just happen to call these three kinds red, blue, and green. Now, we might wonder if color charge is like electric charge, why is it that one is so much more commonly known than the other? A big part of the reason why is that the only sorts of particles that can have a color charge are quarks.

We can recall that there are six varieties of quark, up, down, charm, strange, and top, bottom, and it’s only individual quark particles that can have a certain color of color charge. In general, any of the six quarks can possess any of these three colors of color charge. Just as a few examples, we could have, say, a charm quark with a blue color charge or a down quark, say, with a red color charge or an up quark with a green color charge, or any quark with any color. So, in this lesson, if we see a quark — here, we have a strange quark — colored a particular color, that simply refers to the sort of color charge it possesses.

Now, we know that when we combine quarks, the particles formed out of these combinations are called hadrons. Hadrons themselves are commonly divided into two categories. Mesons are hadrons that are formed of two quarks, specifically one quark and one antiquark. And then baryons are hadrons that are formed by combining exactly three quarks. And it turns out that for both baryons and mesons, when we combine the color charges of the quarks that make up these particles, that charge, we could say, nulls or cancels itself out. This is something that we’ve seen with electric charges. If we combine two equal but opposite charges, the total resulting charge is zero. When we combine color charges, though, and this happens, we don’t say that the total charge is zero; instead, we say the color is now white. This is due to the fact that red and blue and green are what are called the three primary colors, where if we overlap all three, then they result in white.

In the world of color charge then, we could think of white or colorless as a neutral charge. And this brings us back to baryons and mesons because, interestingly, for both of these types of particles, it’s a rule that their overall charge in color terms must be white. That is, the color charge of every baryon and every meson must be neutral or colorless. Here’s an example of how this might work. Say that we have a baryon, a particle made of exactly three quarks. We can see that in this case those quarks are up, down, and down, which means that this baryon is a neutron. In any case, it’s necessary that each one of these quarks has a particular color charge, and it can be red or blue or green. There’s no such thing as a quark with no color charge. So, let’s just assign some charges to these quarks. Let’s just say that the up quark has a green color charge, while the down quark has a blue color charge, and the other one has a red color charge.

Now we might wonder, why did we pick these particular colors for these particular quarks? Partly, it’s just because we had to choose some color charge for each quark. Any one of these quarks could have any of the three color charges. Not only that, but the color charge of a given quark is not fixed over time. So, for example, our up quark, which currently is green, might at some point change to a blue color charge or a red one. But, and this is an important caveat, at any given instant for a baryon, a particle made up of three quarks, at all times one of the quarks must have a green color charge, one must have a blue color charge, and one must have the red. And remember that these names and labels don’t apply to the actual physical color of these quarks; they just describe a kind of charge of which there are three varieties.

Now, the reason that every baryon must at all times have one red, one green, and one blue is that, as we mentioned earlier, a baryon must have a total color charge of white or neutral. When we’re working with three quarks, we only get that when each one represents one of the different colors. So, if at some point, our up quark changed from having a green color charge to a blue color charge, as part of that same process, it will be necessary for our down quark that used to have a blue color charge to change over to green. In this way, the overall neutrality or colorlessness of this baryon is preserved.

Knowing this about baryons, we can also recognize that mesons must follow the same rule of being overall white in their color charge. But a meson, we recall, is made up of a quark and an antiquark. So, how can this color balancing occur then? Well, remember that for every quark, there’s an antiparticle called an antiquark. We can identify the antiquarks by saying that they have the same symbol as their corresponding quark, except for the bar over top of the letter. That bar tells us that in this case, we’re looking at an up antiquark. Just as quarks have what is called a color charge, which could be red or green or blue, so antiquarks have what’s called an anticolor charge.

To understand anticolor charges, we can think of our three color charges in terms of their opposite colors. The opposite color of red, for example, we could call it antired, is commonly known as cyan. When we’re thinking about color charge then, the opposite charge of red is cyan. This means that for a quark with a color charge of red as this down quark has in our neutron, the anticolor charge corresponding to this is cyan. And then likewise, color charges of blue and green have color opposites of yellow and magenta, respectively. Now, just as we said that there are six types of quark and that each type has its own antiparticle, so we say that there are three color charges, red, green, and blue, and that each type has its anticolor charge. So, cyan, yellow, and magenta are not three more kinds of color charges, rather their anticolor charges correspond to the colors we’ve already seen.

We brought all this up because we’re talking about mesons and how it would be possible for the overall color of a meson to be white or neutral. Say that we’re working with this example meson here; it’s made of one up quark and one down antiquark. For mesons, the rule for color charge is this. Whatever the color charge of the quark, and we know there will be just one of those in a meson; let’s just say that in this case, the up quark has a color charge of green, then the antiquark in the meson must possess the anticolor charge of the quark’s color charge. Looking at our color opposites, we see the opposite of green is magenta, and so that is the necessary anticolor charge for our down antiquark to possess.

And now, we can see that this color charge and anticolor charge effectively cancel one another out. In other words, this is a white meson. Note that if we had picked a different color charge for our up quark, say we had picked red, then that would have meant we needed to have a cyan down antiquark. The rule for mesons is that the quark and the antiquark must have color opposites, that is, a corresponding color charge and anticolor charge pair.

All right, so we’ve covered a lot. We’ve learned about this new kind of charge called color charge, of which there are three varieties. And we’ve also seen that it’s quarks that possess color charges, while antiquarks possess what are called anticolor charges. We further asserted that all hadrons, all particles made up of quarks or antiquarks, must have a neutral color charge. This is called white or colorless. We’ve seen how this works for baryons and mesons. And before we get to an example exercise, let’s consider how this works for a particle called an antibaryon.

Knowing that a baryon is a particle that’s made up of exactly three quarks, we might guess than an antibaryon is made up of three antiquarks. And that’s correct. Say that we have an antibaryon made up of an up antiquark, a down antiquark, and a strange antiquark. Just like all individual quarks have a particular color charge, so all individual antiquarks have a particular anticolor charge. We can assign these anticolor charges randomly, knowing that they can change over time.

And let’s say that our up antiquark has an anticolor charge of magenta, our down antiquark has an anticolor charge of yellow, and then our strange antiquark has an anticolor charge of cyan. Knowing that our baryon with three quarks had all three color charges represented, so our antibaryon with three antiquarks has all three anticolor charges represented. This is how an antibaryon satisfies the condition that all hadrons must meet of having an overall charge color, we could say, of white.

Knowing all this about color charge, let’s get some practice through an example exercise.

The diagram shows six baryons in their quark content. The colors of the quarks correspond to their color charge. Which baryons have color configurations that are not possible?

Looking at these six baryons, we see that they’re all made up of three quarks, as baryons must be. We’re told that the colors the quarks take on, and we see that some are red, some are green, and some are blue correspond to the color charge of the quarks. This means that in the diagram a quark colored red, for example, this one, doesn’t indicate that that quark has a positive electrical charge, but instead tells us that the color charge of that quark is red. Along with this, we know that for any color charge, whether red or green or blue, that doesn’t mean the particle with that color charge actually has that color. Rather, this is just a convenient way of talking about how a particle can have one of three kinds of charge.

This means that all of the red-colored quarks we see in these diagrams have a red-color charge, all the green ones have a green-color charge, and so on. In general, any of the six kinds of quark, up, down, charm, strange, and top, bottom, can possess any of the color charges. But, and this is important, whenever we group quarks together to form particles called hadrons, the total or overall color charge of these composite particles must be neutral. This is also called white.

From our knowledge of the primary colors, we know that if we add together red and blue and green, then that gives us the color white. And so, based on the rule that all hadrons must be colorless or must have a total color charge of white, we can say that for any baryon which is a particle made up of exactly three quarks, in order for the total color charge of that Baryon to be colorless or white, it’s necessary that one of the three quarks have a color charge of red, one have a color charge of blue, and the last one have a color charge of green. This is the only way that the total color charge of three quarks can add up to white.

And so, when our question asks which baryons have color configurations that are not possible, we’re looking for those configurations where we don’t have one red, one blue, and one green color charge. We see two examples of that. The fourth baryon shown has two blue color charges and no red, and the fifth one has two red, but no green. These baryons then will not have an overall color charge of white and therefore are not possible color configurations. All the other baryons do have one green, one blue, and one red color charge and therefore are allowed.

Let’s look now at a second example exercise.

The diagram shows six baryons and their quark content. Which of the diagrams do not correctly represent possible quark combinations? How the quarks are colored in the diagrams does not represent their electric charges.

Among these six baryons, we see quarks and antiquarks, and all of them are colored either red or blue or green. We’re told that these colors do not represent electric charges, but they do represent another kind of charge called color charge. Red is one type of color charge, green is another, and blue is a third. In this question overall, we’re on the lookout for any diagrams that do not correctly represent possible quark combinations. Since this diagram is meant to represent six baryons, let’s recall the conditions for quarks coming together to form one of these particles.

The first condition that a baryon must satisfy is that every baryon is made of exactly three quarks. And second, the total color charge of a baryon must be what’s called white. This means that the color charges of the three quarks that combine to form the baryon must add together to form white. If we think about red, green, and blue as primary colors, then we know that if we add them together in equal amounts, the color we’ll end up with is white. For the total color charge of a baryon to be white then, that means it must be made up of equal parts, red, green, and blue color charge. And therefore, each baryon must have one red, one blue, and one green color charge quark. It doesn’t matter which quarks have which particular color charge, but only that they balance out this way.

Considering these two conditions a baryon must satisfy, let’s look again at our six options. We see that choices (ii) and (vi) are both made up of antiquarks rather than quarks. This means that these particles are not technically baryons but instead would be called antibaryons. Since we want to identify which of these diagrams do not correctly represent possible quark combinations, we’ll put options (ii) and (vi) in boxes. And now, let’s look at the second condition a baryon must satisfy, that its total color charge must be white. We can see that options (i), (iii), and (iv) all satisfy this condition in that one of the quarks has a red color charge, one has a blue color charge, and one has a green. But option (v) does not; all of the quarks here have the same red color charge. This means the total color charge of this particle cannot be white, so it does not represent a possible quark combination. The remaining three baryons do show possible combinations.

Let’s summarize now what we’ve learned about color charge. In this lesson, we saw that color charge is a property of quarks analogous to electric charge. There are three types of color charge, red, green, and blue. And each color charge has its corresponding anticolor charge. For red, that’s cyan; for blue, it’s yellow; and for green, it’s magenta. Every quark has a color charge. And any of the six quark types can have any of the three color charge colors. As an extension of this, every antiquark has an anticolor charge.

And lastly, we saw that all hadrons, that is, all particles made of quarks and antiquarks, have an overall color of white. This means that the color charges combined in that composite particle add up to white. For a baryon, this is accomplished by having one red, one blue, and one green color charge, while a meson achieves an overall color of white by pairing a quark with a given color charge with an antiquark that has an opposite color anticolor charge.

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