Red quark going to a red quark via an gluon emission

[Tauk-De]

Hi, I'm currently doing a course in particle physics at masters level and I have this problem:

I know that having an red:anti-red gluon isn't possible as this produces an non-zero trace for its representation, but if I have a red quark that emits a gluon and afterwards is still a red quark, what would be the possible gluon combinations/colors? is it just the two linear combinations: (R:aR - B:aB)/sqrt(2) and (R:aR + B:aB - 2G:aG)/sqrt(6) ?

Thanks in advance

 

[Tauk-De]

never mind I found out

 

[tom.stoer]

... if I have a red quark that emits a gluon and afterwards is still a red quark ...

That's not possible b/c the gluons living in the adjoint rep. of su(3) always change color. A process where the quark color is not affected is possible only in u(3) = su(3) + u(1) where the last u(1) term corresponds to a color-neutral force which would look like QED.

 

[lpetrich]

In a common presentation of SU(3) operator matrices, two of them won't change color, but will give different phases to different colors.

A colorless operator would give the same phase to every color.