# Color function for tetraquark

The color function for tetraquark configuration $$(qq)(\bar{q}\bar{q})$$ is shown following: $$\zeta_1=\frac{1}{2\sqrt6}[(rb+br)(\bar{b}\bar{r}+\bar{r}\bar{b})+(gr+rg)(\bar{g}\bar{r}+\bar{r}\bar{g})+(gb+bg)(\bar{b}\bar{g}+\bar{g}\bar{b})+2(rr)(\bar{r}\bar{r})+2(bb)(\bar{b}\bar{b})+2(gg)(\bar{g}\bar{g})]$$

for $$|6\bar{6}\rangle$$ color $$\text{SU}(3)$$ representation.

However, for example, why is the term $$(rb+br)\bar{r}\bar{r}$$ impossible in $$\zeta_{1}$$?

• ? The $\zeta_1$ color function is color neutral: all colors are neutralized by the respective anticolor. But your "for example" instance has unsaturated b and $\bar r$ indices, so it is not colorless. – Cosmas Zachos Feb 19 at 15:36