# Eight gluons, what are the properties of two of them?

If there are 8 gluons, and 6 of them can be represented as a color/anticolor pair (red/antiblue for example), that leaves 2 "other" gluons. How do these two gluons differ from each other? What happens when two quarks exchange one of these gluons? What happens when two quarks exchange the other of these gluons? Are these two gluons antiparticles of each other? What nonzero properties do they have?

If they are colorless, can they exist in isolation?

• There are nine possible color-anticolor pairs. – G. Smith Aug 24 '20 at 5:25
• As I understand it, color neutral (color same as anticolor) is a disallowed 'singlet' state. I think I understood the reason it is disallowed but I don't remember it now. – Madman Aug 24 '20 at 5:27
• Are these two gluons antiparticles of each other? All 8 gluons are their own antiparticles. See en.wikipedia.org/wiki/Gluon#Eight_colors – G. Smith Aug 24 '20 at 5:27
• Regarding the singlet, see en.wikipedia.org/wiki/Gluon#Color_singlet_states – G. Smith Aug 24 '20 at 5:30
• I am somewhat confused by en.wikipedia.org/wiki/Gluon#Eight_colors : They show 6 of them somewhat like having 6 colors but apparently as two states opposite each other (r\bar{b}+b\bar{r} is this to force them to be colorless? I thought only one part would be used. The other two are odd: r\bar{r}-b\bar{b} and r\bar{r}+b\bar{b}-2g\bar{g}. It's not symmetrical. I guess I just don't get the concept of adding states and especially multiplying them by the square root of 2. – Madman Aug 24 '20 at 20:06

All eight color states for gluons are equivalent in the sense they they are linearly-independent non-singlet color-anticolor states. You can pick any basis you want in this 8-dimensional color-anticolor space, and how you do it makes no physical difference.

(Why eight? Because three color states times three anticolor states minus one colorless singlet state leaves eight colorful color-anticolor states.)

So there are no “other” gluons. None of them are special in any way, just like neither the $$xy$$ nor $$xz$$ nor $$yz$$ plane in Euclidean space is special.

All gluons have color, so none exist in isolation. All have spin $$1$$, and in the conventional basis all are their own antiparticle.

An analogy: you can view the $$W^3$$ of $$SU(2)$$ as the counterpart of the "2 other gluons" of $$SU(3)$$.

The weak $$SU(2)$$ has 3 "gluons": $$W^1, W^2, W^3.$$ As @G. Smith pointed out in the other answer, they are "equivalent" in the sense of Lie algebra.

However, when you pick out a specific direction (representation) to define the iso-spin up and down states $$|\pm>$$, say $$W^3 |\pm> = \pm |\pm>,$$ then there is a diffidence between the 3 gluons: $$W^1$$ and $$W^2$$ (or their combinations $$W^+$$ and $$W^-$$) can flip the "color" (iso-spin), while $$W^3$$ will not change the "color" (iso-spin). Therefore, you can make an analogy between the $$W^3$$ of $$SU(2)$$ and the "2 other gluons" of $$SU(3)$$.

For the case of weak $$SU(2)$$, Mother nature took a liking to a specific iso-spin direction via the Higgs mechanism and we can tell apart an electron and a neutrino. When it comes to strong $$SU(3)$$, she is impartial (color blind). Any specific color assignment scheme is just a human construct.

• I think this makes sense. For the weak system there are two bosons that affect charge as well as weak stuff and one much like the "odd" gluons that doesn't, and Nature has a preference via the Higgs mechanism so the first becomes W+ and W- and the third the Z.And for gluons there's more going on because of 3 colors so 6 color related and two not color related? And no Higgs mechanism so none come out as different? – Madman Aug 24 '20 at 20:17
• 6 color related and two not color related? Even after reading both answers, you still think this? – G. Smith Aug 25 '20 at 0:42
• Yes I shouldn't have written that. I was more thinking of the W+/W- vs, the Z where the Ws transfer charge and the Zs don't. I do understand (sort of, I guess) that unlike the weak force the strong force doesn't have a preferred direction so gluons don't have a preferred viewpoint. – Madman Aug 25 '20 at 14:38