Experimental evidence for color-neutral gluons $( (r\bar{r}−b\bar{b})$ and $(r\bar{r}+b\bar{b}−2g\bar{g}) )$ Is there any experiment/measurement that would have a different outcome if one of the following scenarios is applied:


*

*The two color-neutral** gluons would not exist

*Those gluons would have very large masses


** we are talking about the 2 gluons not exchanging color, conventionally written as
$(r\bar{r}−b\bar{b})/\sqrt2$
$(r\bar{r}+b\bar{b}−2g\bar{g})/\sqrt6$
EDIT:
Since I am now aware that 'color-neutral' does not exist, the question only makes sense if stated as
'What would be the experimental evidence if color-symmetry was broken in some way? (such that 2 of the gluons were singled out)'
 A: Because the color charge is an exact symmetry (there is no "color mass hierarchy" as there is with neutrino flavor) and because colored objects are confined, I don't know that there is experimental evidence for any particular gluon. The evidence is that hadrons have an internal degree of freedom which can be described by the $SU(3)$ symmetry group; we call it "color" mostly because the other is quite a mouthful.
One feature of color as an exact symmetry is that rotations among the different color charges give the same physics. So for instance we could make the substitution
\begin{align*}
r' &= \frac{r + b}{\sqrt2} \\
b' &= \frac{r - b}{\sqrt2} \\
g' &= g
\end{align*}
and similarly for the anticolors. The "colorless" gluons in this basis can be represented in the original basis
\begin{align}
\frac{r'\bar r' - b'\bar b'}{\sqrt2} &=
\frac1{\sqrt2}\left( 
\frac{r + b}{\sqrt2} \frac{\bar r + \bar b}{\sqrt2}
-
\frac{r - b}{\sqrt2} \frac{\bar r - \bar b}{\sqrt2}
\right)
=
\frac{r\bar b + b\bar r}{\sqrt2}
\end{align}
as a coherent superposition of color-changing gluons.
If we had some very massive or missing gluons, color symmetry would no longer be exact; there would probably be a favored color, and I'm not sure that you could still have the complete color confinement that we observe in the real world.
