Undergrad Quark flavor and color independent?

[friend]

Each quark as a flavor charge and a color charge. Are these two properties totally independent of each other? Thanks.

 

[mfb]

Yes.

 

[friend]

Yes.

So, for example an up quark, u, can have any of the following colors: red, green, blue, anti-red, anti-green, and anti-blue? And an anti-up quark, u, can have any of those colors or anti-colors, too. Is this right? Thanks.

PS. how do I do an overstrike in this forum?

 

[Orodruin]

So, for example an up quark, u, can have any of the following colors: red, green, blue, anti-red, anti-green, and anti-blue?

No, a quark cannot carry anti-colour. It is in the $\bf 3$ representation of SU(3), not in the $\bf \bar 3$ representation.

 

[friend]

No, a quark cannot carry anti-colour. It is in the $\bf 3$ representation of SU(3), not in the $\bf \bar 3$ representation.

OK. So now I'm learning something (I think). Correct me if I'm wrong. Quarks of any flavor or anti-flavor, e.g., $u$ or $\bar u$, can only have red, greed, or blue color. But only the gluons can have anti-color in combination with a color. Is this right? Thanks ever so much.

 

[friend]

OK. So now I'm learning something (I think). Correct me if I'm wrong. Quarks of any flavor or anti-flavor, e.g., $u$ or $\bar u$, can only have red, greed, or blue color. But only the gluons can have anti-color in combination with a color. Is this right? Thanks ever so much.

I think there needs to be a correction. I found this site and similar that says quarks have a color charge (red, green, blue), but anti-quarks have anti-color (anti-red, anti-green, anti-blue). The link given is to a site claiming to be sponsored by DOE and NSF. If this is not credible, can someone point me to a more reliable source that confirms this? Thanks.

 

[Orodruin]

Yes, anti-quarks transform according to $\bf\bar 3$. Gluons transform according to the adjoint representation $\bf 8$ and gluons are therefore traceless colour-anticolour combinations.

 

[friend]

On the Wikipedia site for quarks, I found this diagram. There is no reference to individual quarks. But it does seem to suggest that a gluon travels only from one type of quark to its anti-quark version. For example, in the diagram, the $g$^{$g\bar b$} gluon is between the $q$^$g$ quark and the $\bar q$^$b$ anti-quark. Does this mean that the $g$^{$g\bar b$} gluon must travel between any quark of color green and any anti-quark of color blue? (I thought anti-quarks can only have anti-color.) Or does this mean that the $g$^{$g\bar b$} gluon can only travel between a $u$ quark and a $\bar u$ anti-quark, or can only travel between a $d$ quark and a $\bar d$ anti-quark, or can only travel between a $s$ quark and a $\bar s$ anti-quark, etc? I'd appreciate any help in reading this diagram. Thanks.

 

[mfb]

But it does seem to suggest that a gluon travels only from one type of quark to its anti-quark version.

No, and I don't know how you got that idea. Check Feynman diagrams of gluon exchange.

Does this mean that the $g$^{$g\bar b$} gluon must travel between any quark of color green and any anti-quark of color blue?

No.

(I thought anti-quarks can only have anti-color.)

Correct.

 

[Orodruin]

That diagram is group-theoretical in origin and shows the charges under the diagonal SU(3) generators. It has nothing to do with gluons "travelling" between quarks. In order to understand the diagram you need to understand group representation theory, which it is not clear to me from this thread if you do or not.

Also note that when you encounter Feynman diagrams they are really not pictures of particles flying around (although physicists will often talk about them in a manner that might suggest that to a layman), they are graphical representations of mathematical terms in a series expansion. There is also some caveats for representing colour in Feynman diagrams ...

 

[friend]

I don't see the problem. Use whatever language you're would like. I'm sure things can get complicated with superpositions and different basis. But the language used in the figure means something. Correct me if I'm wrong, but it seems obvious that $\bar q$ is an anti-quark whereas $q$ is a quark. The down pointing blue triangle must mean anti-blue, since anti-quarks on take only anti-colors. And the $g\bar b$ in the symbol $g$^{$g\bar b$} seems to indicate what color is being changed by that gluon. If someone could explain what pair of quarks can possibly be changed by $g$^{$g\bar b$} and how they are changed, this would be very helpful.

 

[friend]

This video seems to be in the same spirit as the diagram above. The author is Dr. Vitaly Velizhanin. I'm sure it's probably an oversimplification. But is it actually wrong? Does it neglect other possible interactions with any of the gluons it depicts? For it seems to depict a gluon of a certain color/anti-color coming from only one type of quark and being accepted by only one other type of quark. Thanks.