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Color factor

  1. Jun 11, 2015 #1
    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.
     
    Last edited: Jun 11, 2015
  2. jcsd
  3. Jun 11, 2015 #2

    ChrisVer

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    Gold Member

    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)
     
  4. Jun 11, 2015 #3
    I think it's simple like that .. thanks.
     
  5. Jun 12, 2015 #4
    Hi,

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