Help me to understand the QCD vertex factor

In summary, the conversation is about understanding the 3-vertex and 4-vertex factors of non-abelian and QCD fields from Peskin & Schroeder page 507. The person is latexing equations and needs help understanding how to derive these vertex factors by permuting group indices and momentum and Lorentz indices. They have already expanded the Lagrangian density but are having trouble computing the terms.
  • #1
moss
49
2
Guys...help me out to understand this 3-vertex factor of non-abelian and or QCD fields.
it is from peskin & schroeder page 507.
 
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  • #2
What specifically don't you understand?
 
  • #3
vanhees71 said:
What specifically don't you understand?
i am latexing the 2 equations in a minute that i need help for.
 
  • #4
Guys...help me out to understand this 3-vertex factor of non-abelian and or QCD fields
and then the 4-vertex of the same fields, it is from peskin & schroeder page 507.

I want to understand how to get the following vertex factors.
The equation are as follows;\begin{equation}

eq-1=gf^{abc}[g^{\mu\nu}(k-p)^{\rho}+g^{\nu\rho}(p-q)^{\mu}+g^{\rho\mu}(q-k)^{\nu}]

\end{equation}

\begin{equation}

eq-2=-ig^{2}[f^{abc}f^{cde}(g^{\mu\nu}g^{\nu\sigma}-g^{\mu\sigma}g^{\nu\rho})+f^{ace}f^{bde}(g^{\mu\nu}g^{\rho\sigma}-g^{\mu\sigma}g^{\nu\rho})+f^{ade}f^{bce}(g^{\mu\nu}g^{\rho\sigma}-g^{\mu\rho}g^{\nu\sigma})]

\end{equation}
 
  • #5
You should be able to derive these interaction terms by expanding the Lagrangian density in the fields as usual.
 
  • #6
yes, I expanded just the lagrangian propotional to 1/4tr(G)^2 and got the 3 and 4 vertex terms. what I am confused is that
how do I get these terms by permutation of what? the group indices a,b,c,?

Bailin and Love says on page 127 that permutation of momentum and lorentz indices will give these vertex factors
but I am having problem in computing it.
 

Related to Help me to understand the QCD vertex factor

1. What is the QCD vertex factor?

The QCD vertex factor is a fundamental concept in particle physics that describes the interaction between quarks and gluons. It is part of the theory known as Quantum Chromodynamics (QCD) which explains the strong nuclear force that holds quarks together to form protons and neutrons.

2. How is the QCD vertex factor calculated?

The QCD vertex factor is calculated using Feynman diagrams, which are graphical representations of particle interactions. The vertex factor is determined by the coupling strength between the quarks and gluons, and is dependent on the energy and momentum of the particles involved.

3. What role does the QCD vertex factor play in particle interactions?

The QCD vertex factor is crucial in understanding and predicting the behavior of subatomic particles. It determines the strength of the interaction between quarks and gluons, and can also give insight into the mass and spin of particles.

4. How does the QCD vertex factor relate to the strong nuclear force?

The QCD vertex factor is directly related to the strong nuclear force, which is one of the four fundamental forces in nature. This force is responsible for binding quarks together, and the QCD vertex factor helps to explain the nature of this binding.

5. Are there any current research developments or applications related to the QCD vertex factor?

Yes, there is ongoing research in the field of QCD and the vertex factor. This includes efforts to better understand the properties of the Higgs boson, as well as studying the behavior of quarks and gluons in extreme conditions such as in the early universe or in high-energy collisions at particle accelerators.

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