Understanding Color Factors in Feynman Diagrams

[Safinaz]

Hi there,

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.

 

[ChrisVer]

I think you can also have $Tr(T^a T^c T^b)$... in particular you add them...
However I'm not sure (I only guessed it because of the symmetry of the loop, top can go from vertices named as a->b->c or vertices a->c->b without changing it)

 

[Safinaz]

I think it's simple like that .. thanks.

 

[Safinaz]

Hi,

Regarding c_2 (eq. 27) in that paper, i think it's more serious, have you an idea how to get it ?