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In paper as :

http://authors.library.caltech.edu/8947/1/GREprd07.pdf

I don't understand the colour factor associated with two gluons and single octet scalar as the first Feynman diagram in fig. 3 ?

In eq. 27, this colour factor is given by ## (d^{abc})^2 ## .. so, how did this come ?

I think the matrix amplitude in the first Feynman diagram in fig. 3 is proportional with:

## T^a_{i i'} T^b_{i' i''} T^c_{i'' i} ##,

how this will turn to anti commutator of two of the generators, which I think are: ## T^b ## and ## T^c ## (to give then ## d^{abc}= tr (T^a \{ T^b, T^c \}) ~##) ..

Best.

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# Color factor

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