In quantum chromodynamics, in an interaction in which a quark and an anti-quark exchange a gluon, the color charge must be conserved. When we are talking about base states like $r\bar{b}$ it seems simple to understand what this means, but when we talk about mixed states like $(r\bar{b} + b\bar{r})/\sqrt{2}$, I don't understand it clearly.
If the quark-antiquark pair are in state $(r\bar{b} + b\bar{r})/\sqrt{2}$ before the interaction, how can I compute the total color charge to conclude which are the possible states after the interaction? To exemplify, is the state $(r\bar{r} + b\bar{b})/\sqrt{2}$ a possible state after this interaction?
Additionally, if I have the initial state and the final state of the pair respecting color charge conservation, how can I compute the state of the gluon that was exchanged in the interaction?
