# Questions about the gluons, their color and anti-color charges and charge of quarks

by WilliamJ
Tags: anticolor, charge, charges, color, gluons, quarks
 P: 13 I have been learning some stuff off of youtube, but I did not get a full enough understanding of how quarks have colors, and anti-quarks have anti-colors and how the gluons have to be colors and anti-colors and how it all works. Some of it doesn't make any sense. The first question is about a red quark absorbing an red-antiblue quark and turning blue. I don't see how a gluon of red-anti-blue quark makes the red quark suddenly turn blue, not anti-blue, but I have heard that the quarks can only have a regular color and an anti-quark are the only quarks that can have an anti-color. "As a quark absorbs a gluon, it keeps its status as a quark or anti-quark. So what does that mean? Also, if a blue quark ineracts with another quark of a different color say red, the qluon is transfered and the quarks swap their colors. This means that when two quarks exchange a gluon, they switch their colors, but what about when they are exchanging gluons that are like the red and and antiblue quarks? I don't even know how to address the question. And the question lingers, what about quarks and anti-quarks and gluons that are colors and ant-colors and how they relate? The whole thing of quarks and anti-quarks exchanging gluons which have a color and an anti-color and how only quarks can exchange colors with other quarks, and anti-quarks exchange anti-colors with anti-colors, by gluons which have a color and an anti-color makes no sense to me. Sorry if this sounds so confusing, but the reason is is that I am confused about it. If there is anyone out there who would answer my question in a way that clears up the confusion, I would appreciate it. Sincerely, WilliamJ
 Sci Advisor Thanks P: 4,160 Here's a diagram from Carl Brannen's site that explains it. Looks complicated at first, but shows it better than any other diagram I can find. Time goes from left to right. Color is conserved, which means that if you pick a red line say, you can follow it all the way through the diagram and come out the other side. Quarks are represented by single lines and have one color. If the arrow points to the right it's a quark, if it points to the left it's an anti-quark. Gluons are represented by wavy lines and have two colors. If you draw arrows on the colored lines in a gluon you'll see that one arrow points to the right (a "color") and the other arrow points to the left (an "anti-color") At the left we initially have three quarks, red green and blue. The first thing that happens is that that the green quark emits a green anti-red gluon. The green anti-red gluon strikes a red quark and turns it into a green quark. And so on!
P: 136
 Quote by WilliamJ ...The first question is about a red quark absorbing an red-antiblue quark and turning blue. I don't see how a gluon of red-anti-blue quark makes the red quark suddenly turn blue, not anti-blue...
You're right, this particular scenario cannot occur. A red quark could emit a red-antiblue gluon to become a blue quark - sort of like "+red - (+red + -blue) = +blue" - but for a red quark to become blue by absorbing a gluon the latter must be blue-antired.
 ...but I have heard that the quarks can only have a regular color and an anti-quark are the only quarks that can have an anti-color. "As a quark absorbs a gluon, it keeps its status as a quark or anti-quark. So what does that mean?
It means that, apart from its colour, all of the other charges and internal quantum numbers of the quark remain the same. Eg if its flavour is up it remains up. And, in particular, gluons cannot change quarks into antiquarks, just as photons cannot change (eg) electrons into positrons.
 Also, if a blue quark ineracts with another quark of a different color say red, the qluon is transfered and the quarks swap their colors. This means that when two quarks exchange a gluon, they switch their colors, but what about when they are exchanging gluons that are like the red and and antiblue quarks?
This is one and the same thing - quarks change colours by exchanging gluons. The word "exchanging" as used here is not intended to imply that each interaction involves sending gluons in both direction. Only one gluon need be transferred in each interaction.

Gluons can be also exchanged between a quark and an anti-quark. For example a green quark can emit a green-antiblue gluon (thus becoming blue) and the gluon can then be absorbed by an antigreen antiquark, turning the latter antiblue. This is a typical interaction within a meson - notice how the anti-quark both starts and ends having the anti- of the quark's colour.
 ...And the question lingers, what about quarks and anti-quarks and gluons that are colors and ant-colors and how they relate?
The simple picture of red-antiblue type gluons unfortunately isn't the whole story.

In fact, in addition to the six gluons of the colour - anti-other-colour combinations, there are two further ones which can loosely be described as "neutral". Their colour combinations can be described mathematically as
$1\ /\ \sqrt{2}\ (r\bar{r}\ -\ g\bar{g})\ \ \ \$and$\ \ \ \ 1\ /\ \sqrt{6}\ (r\bar{r}\ +\ g\bar{g}\ -\ 2b\bar{b})$
These can be exchanged between any quarks or anti-quarks that have at least one of their (anti-)colours.

Even the above, however, is still a very oversimplified picture. To really understand this you really do have to have at least a basic understanding of the SU(3) symmetry group. There is quite a good introduction to gluon types and exchanges in "Elementary Particle Physics" by Alessandro Bettini.

 P: 13 I know that this is a lot to ask, but I am having an unusually difficult time learning about the strong force, and I see that you are very knowledgeable about this topic, enough to help me make sense of it all. I really need some help with this so if you could help explain it to me I’d appreciate it. I do not understand how this diagram works. I don’t even really have words to describe the questions I have about it. Is this diagram a standard diagram of how all quarks exchange their colors? I see that the straight lines represent quarks with their different colors, and I can see how the gluons have color/anti-color combinations that exchange the colors between quarks in a way, but I still don’t completely get it. I see that a line (quarks?) that point to the right is a quark, and that a line that points to the left is called an anti-quark. However, the only line that points left in this diagram is the green on the bottom right of the diagram which is part of the circle with the green and red quarks have their colors going in opposite directions. The thing is, is that I have heard from youtube.com that (as far as I can remember) only anti-quarks can have anti-colors and the part of the diagram I have just talked about right before this sentence states basically (when looking at the diagram) that there is one possible anti-particle in this diagram. Yet again, is this diagram a standard illustration? It doesn’t seem so because of the fact that there is only one anti-quark in this diagram as far as I can tell. Also from the diagram and from what you have said is that “Color is conserved, which means that if you pick a red line say, you can follow it all the way through the diagram and come out the other side.” I don’t see how this is, but then again, I am having a hard time making sense of this. I understand that the gluons come in color/anti-color combinations, and that has to do with the changes of colors between the different colored quarks. “You wrote this:”At the left we initially have three quarks, red green and blue. The first thing that happens is that that the green quark emits a green anti-red gluon. The green anti-red gluon strikes a red quark and turns it into a green quark. And so on!” Then you can have a red quark emit a green anti-red gluon, this green anti-red gluon is then absorbed by a green quark and turn it red, but how do you deal with the place where there is a green anti-quark in the diagram. Also, how do you follow each one of the colors, one at a time through the diagram, from the left to the right, how is color charge conserved, and in what way does the conservation of color charge resemble the conservation of electric charge?
Thanks
P: 4,160
WilliamJ, There's no special significance to the diagram that Brannen drew. It's just a random sample of what might happen, consistent with the rules. Three quarks are incoming on the left, three quarks are outgoing on the right. So it depicts a proton that comes in, bounces around awhile, and then continues on its way. It would be more interesting to show a proton emitting a pion or something, but I couldn't find any like that.
 Also, how do you follow each one of the colors, one at a time through the diagram, from the left to the right, how is color charge conserved, and in what way does the conservation of color charge resemble the conservation of electric charge?
This is the easy part. Place your pencil at the beginning of the red line and follow it. It just keeps on going. It never dead ends, and it never forks into two red lines. This illustrates color charge conservation, showing that "red color" is never created or destroyed.

You're right, there's only one anti-quark in the picture, the green one at the loop marked A. Green moving to the left is called 'anti-green'. Inside each of the gluons there is one line moving to the right (the color) and another one moving to the left (the anti-color).
P: 136
 Quote by WilliamJ These are the questions I have about your reply. I noticed that at the end of the reply some equations were written that I did not have the foggiest idea of what to make of them. You are much more advanced, so if you reply, make sure to keep it really simple...
Unfortunately it just isn't possible to answer all your questions in layman's language, but here are a couple of things.
 Red quarks emit a red-antiblue gluon and becomes a blue quark. “+red – (+red + -blue) = +blue” Red quarks absorb a blue-antired quark and becomes a blue quark. What is the equation here?
“+red + (-red + +blue) = +blue”

As you may have guessed, a red-antiblue gluon is just the antiparticle of the blue-antired one.
 ... I know that particles and antiparticles can pop up, created in pairs, like when a gama ray with at least 1.02 MeV can create electrons and positrons. This is called pair production.
Yes, and gluons can do this too. For example our red-antigreen gluon can produce a red quark together with a green antiquark. But both must be of the same flavour, eg up and anti-up, down and anti-down, etc. The quark must take the gluon's colour, and the anti-quark its anti-colour.

A further twist is that, unlike photons which carry no electric charge, gluons carry colour charges so can also interact with other gluons. For example a red-antiblue gluon can emit a red-antigreen gluon and in doing so become green-antiblue. This makes a huge difference to the physical phenomena that result from the strong force, and is ultimately the reason why quarks and anti-quarks are always confined within hadrons, and can never be observed alone.
 P: 13 Gluons come in antiparticles. For example, red-antiblue gluon in the antiparticle of the blue anti-red. Red quarks emit a red-antiblue gluon and becomes a blue quark. 1) +red - (+red + -blue) = +blue Red quarks absorb a blue-antired quark and becomes a blue quark 2) +red + ( -red + +blue) = +blue What happens to the opposite of 1), where the red quark emits the gluon, when the scenario turns into absorption. What happens to the opposite of 2), where the red quark absorbs the gluon, when the scenario is turned into emission. Are in this example between 1 and 2, do gluons and anti-gluons such the same even if the emission or absorption change I mentioned I see that a gluon of a color-anticolor can cause a quark and its antiquark, like up and anti-up and down and anti-down, etc. The antiquarks get the anticolors and the regular quark gets the regular color. Why is this set up w/only a quark and its antiquark? Is this a particular category of mesons? Are quarks and anti-quarks like u and anti-up an example of flavors, not like up and down? I don’t really understand how gluons interact and change the gluon colors. Which would be very beneficial to me to see examples of emission/absorption, basically many examples of the color changes by the gluons. If I actually see examples of how the quarks change colors and gluon charges, it will finally sink in. I hope this isn’t too redundant. I should already know the answer by how many replies I’ve gotten. Most things I get really easily about particle physics that I have been learning so about for so long, the whole color charge, etc. is a particularly difficult to master subject. Sincerely, WilliamJ
P: 136
 Quote by WilliamJ Gluons come in antiparticles. For example, red-antiblue gluon in the antiparticle of the blue anti-red. Red quarks emit a red-antiblue gluon and becomes a blue quark. 1) +red - (+red + -blue) = +blue Red quarks absorb a blue-antired quark and becomes a blue quark 2) +red + ( -red + +blue) = +blue What happens to the opposite of 1), where the red quark emits the gluon, when the scenario turns into absorption. What happens to the opposite of 2), where the red quark absorbs the gluon, when the scenario is turned into emission...
If by "the opposite of 1)" you mean a red quark absorbing a red-antiblue gluon, then, as I mentioned originally, it can't. That gluon can be absorbed only by (a) a blue quark (which then becomes red), (b) an antired antiquark, which then becomes antiblue, or (c) another gluon.
 ...I see that a gluon of a color-anticolor can cause a quark and its antiquark, like up and anti-up and down and anti-down, etc. The antiquarks get the anticolors and the regular quark gets the regular color. Why is this set up w/only a quark and its antiquark?
Very similar to why a photon can pair-produce e+e-, but not e+e+, e-e- or μ+e-. This is down to the conservation of (a) charges, and (b) baryon and lepton type numbers (respectively). Quarks have electric charges, but gluons none, so the total electric charge of the daughter particles must also be zero. An antiquark of course has the opposite electric charge to that of its quark counterpart (same flavour). All quarks also carry a 'flavour' number of ±1* (eg "up-ness", charm, strangeness, etc), antiquarks the opposite, and gluons again zero. (Electrons have electron number +1, positrons -1, and photons 0.) These quantum numbers are also conserved in all strong and electromagnetic interactions.

* by convention, the sign of a quark's flavour number is the same as that of its electric charge, and the corresponding antiquark's is the opposite. So for example a s quark has strangeness -1, and its antiquark +1, whereas c has charm +1, etc.
 ...Is this a particular category of mesons? Are quarks and anti-quarks like u and anti-up an example of flavors, not like up and down?
Mesons are composite particles formed from one valence quark and a valence antiquark. These then surround themselves with a cloud of virtual gluons and other quark/antiquark pairs.

The six quark flavours are up, down, charm, strange, top and bottom. Each has its corresponding anti. The flavours are commonly abbreviated to their initial letters, such as u or d. u, c and t have electric charge +2/3 and may collectively be referred to as 'up-type'. d, s and b have -1/3 and are sometimes called 'down-type'.

In a meson, the valence quark and antiquark must have opposite colours, but need not be of matching flavours. For example a π+ meson is an up with an anti-down - note the charges are +2/3 -(-1/3) = +1. It also has upness of +1 and downness of +1. (Historically, upness and downness were combined into another quantum number called isospin, whose numerical value is half the total upness and downness.)
 ...I don’t really understand how gluons interact and change the gluon colors. Which would be very beneficial to me to see examples of emission/absorption, basically many examples of the color changes by the gluons. If I actually see examples of how the quarks change colors and gluon charges, it will finally sink in. I hope this isn’t too redundant. I should already know the answer by how many replies I’ve gotten. Most things I get really easily about particle physics that I have been learning so about for so long, the whole color charge, etc. is a particularly difficult to master subject.
Yes, unfortunately you do need to study the maths of SU(3) to really understand this deeply.
 P: 13 When quarks change colors would the following be an example of how all quarks change color charge? Red Turns Into Blue: red - (red + -blue) = blue blue + (red + -blue) = red Blue Turning Into Red: blue - (blue + -red) = red red + (blue + -red) = blue
 P: 13 Am I completely wrong? I need to know exactly how to illustrate the color changes between quarks, with the addition and subtraction, like the absorption and emission, the example given. Do I have them in the wrong pairs, like may be all of the emissions and absorptions of red need to be in one group, and all of the emissions and absroptions of blue need to be in one group?. I need to know whether I did it right or if I did it wrong, and if I did it wrong, how is it supposed to be denoted to describe the color exchange between quarks?
 P: 13 I think I understand how a red quark can absorb a gluon turning it blue, and how a red quark can emit an anti-gluon and turn blue, but that in both situations there is only a red quark changing into blue, not swapping out colors between two quarks. For example: red - (red +-blue) = blue red + (blue -red) = blue These are the two original red colored quarks which turn blue. But how can you combine different emissions and absorptions like denoted here, to make it show how two quarks can exchange colors? I'm still needing a bit of clarification.
 Mentor P: 11,617 Think about it like this: In every reaction, the sum "red minus antired" (and similar for blue and green) is conserved, which means that it is the same before and after the reaction. Therefore, a red quark can emit a (red, anti-blue) gluon and become blue: Before the reaction, we have 1 red (quark) and 0 blue. After the reaction, we have 1 red (in gluon) and 1-1=0 blue (blue in quark, anti-blue in gluon). This is another way to express "red = (red-blue)+blue", where (red-blue) is the gluon. The left side has the initial state (the red quark) and the right side has the final state (gluon+quark). Now, this (red, antiblue) gluon can be absorbed by a blue quark, which becomes red: "blue + (red-blue) = red" This image has this process: It is below the "C". The horizontal axis is time. Of course, this is just a model, and should not be taken too seriously. It is not meaningful to say "at time x, this quark emitted a gluon which hit another quark later".