Is there a blue-anti blue gluon?

[saif gaber]

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.

 

[jedishrfu]

Welcome to PF!

There is some discussion of gluons here:

http://en.wikipedia.org/wiki/Gluons

where they talk about the reasoning of why there's no blue anti-blue gluon

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".

...

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.

 

[samalkhaiat]

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.

The "colorless" blue-antiblue appears as a component in two of the 8 quarks:
$$|8_{ 3 } \rangle = \frac{ 1 }{ \sqrt{2} } ( r \bar{ r } - b \bar{ b } )$$
$$|8_{ 8 } \rangle = \frac{ 1 }{ \sqrt{6} } ( r \bar{ r } + b \bar{ b } - 2 g \bar{ g } )$$
These are the two "colorless" members of the quark octet $[8]$.

Are asking about the color singlet? which is
$$|1 \rangle = \frac{ 1 }{ \sqrt{3} } ( r \bar{ r } + b \bar{ b } + g \bar{ g } )$$

If this singlet state existed, it would be as common as the photon! It would also add a big contribution to the force of gravity! So there are both theoretical and experimental reasons to rule it out.

Sam