The discussion centers on the existence of blue-anti blue gluons within quantum chromodynamics (QCD). It is established that there are eight independent color states of gluons, which are represented by the color octet, and blue-anti blue gluons do not exist due to the linear independence of these states. The Gell-Mann matrices illustrate the relationships between color states, confirming that combinations like blue-anti blue cannot produce a singlet state. Theoretical and experimental evidence supports the conclusion that the color singlet state, which would include blue-anti blue gluons, is ruled out.
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There are eight remaining independent color states, which correspond to the "eight types" or "eight colors" of gluons. Because states can be mixed together as discussed above, there are many ways of presenting these states, which are known as the "color octet".
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These are equivalent to the Gell-Mann matrices; the translation between the two is that red-anti-red is the upper-left matrix entry, red-anti-blue is the upper middle entry, blue-anti-green is the middle right entry, and so on.
The critical feature of these particular eight states is that they are linearly independent, and also independent of the singlet state; there is no way to add any combination of states to produce any other.
(It is also impossible to add them to make red-anti-red, green-anti-green, or blue-anti-blue otherwise the forbidden singlet state could also be made.)
There are many other possible choices, but all are mathematically equivalent, at least equally complex, and give the same physical results.
saif gaber said:the only reason i am not sure about the existence of blue-anti blue gluons is because i have never seen them in any of the explanations i have read or watched and that is what confuses me.