|MadSci Network: Physics|
You seem to have a picture of gluons which to some extent misses the point. In the following I will try to convince you that the question you should have asked is "Why are there eight instead of nine gluons?" instead of "Why are there eight instead of six?".
QCD, the theory of strong interactions, is based on the notion that there are three colours with their corresponding anti-colours. Observable particles must be colour singlets, which means that any colour transformation you could devise must leave the colour state of the particle unaltered (think of colour transformations as rotations in three-dimensional space - this is a very rough but sufficient analogy for our purpose). Quarks are unobservable because each one carries overall colour; they are no colour singlets. On the other hand you must not forget that we are talking quantum theory here: It is possible to combine states of different colour in a linear way. One can e.g. construct a colour singlet quark-antiquark state by taking (green-charm,antigreen-charm) plus (red-charm,antired-charm) plus (blue-charm,antiblue-charm), getting the J/psi meson. Something like (red-quark,antired-quark) may seem like an uncoloured item, but is in fact not a colour singlet. This misunderstanding emerges from the fact that in ordinary electrodynamics one has only one single charge (the electric charge) and not three. So above state is in fact `red-neutral', but not a colour singlet.
Now what about the gluons? In the light of the previous paragraph one might be tempted to state that there must in fact be nine gluons, each one carrying some charge and some anticharge: 3x3=9. But why are there only eight? Well, there is one and only one way to combine gluons so that the resulting object is a colour singlet and so does not qualify for QCD interactions: (red,antired)+(blue,antiblue)+(green,antigreen) This gluon is a colour singlet and thus reduces the number of `interacting', i.e. physically significant gluons, to eight.
Hope that helps. For further studies I recommend the excellent book `Particle Physics: A Los Alamos Primer' by N.G. Cooper (ed).
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