Understanding Color Factors in Feynman Diagrams

In summary, the conversation discusses the color factor associated with two gluons and a single octet scalar in the first Feynman diagram in figure 3 of the referenced paper. The color factor is given by (d^{abc})^2 in equation 27, but it is unclear how this was derived. The matrix amplitude in the first Feynman diagram is also discussed and it is suggested that it is proportional to the anti-commutator of two generators, T^b and T^c. The possibility of using Tr(T^a T^c T^b) is also mentioned. Finally, there is a question about how to obtain c_2 (eq. 27) in the paper.
  • #1
Safinaz
261
8
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.
 
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  • #2
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)
 
  • #3
I think it's simple like that .. thanks.
 
  • #4
Hi,

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

FAQ: Understanding Color Factors in Feynman Diagrams

What are Feynman diagrams and why are they important in understanding color factors?

Feynman diagrams are visual representations of particle interactions in quantum field theory. They are important in understanding color factors because they show the exchange of "color charges" between particles, which is essential for explaining the behavior of subatomic particles.

How do color factors affect the outcome of particle interactions in Feynman diagrams?

Color factors determine the strength and type of interaction between particles in Feynman diagrams. The exchange of color charges can lead to different outcomes, such as annihilation or scattering, depending on the colors involved.

What is the significance of the color charge in Feynman diagrams?

The color charge is a fundamental property of subatomic particles that describes their strong nuclear force. In Feynman diagrams, it is represented by lines and arrows that show the exchange of color charges between particles.

How do we represent color factors in Feynman diagrams?

Color factors are represented by the color and direction of the lines and arrows in Feynman diagrams. For example, a red line represents a particle with a red color charge, while an anti-red line represents the exchange of an anti-red color charge.

Are there any limitations to using Feynman diagrams to understand color factors?

Feynman diagrams are a useful tool for understanding color factors, but they have limitations. They only show the exchange of color charges between particles and do not account for other factors such as spin or mass. Additionally, they can become increasingly complex when multiple particles and interactions are involved.

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