Problem with Feynman Rule for Vertices

[Neitrino]

Dear PF,
I would like to thank you for existence of Physics forums since it appears very helpful.

Dear PF,
I was reading one paper and trying to derive Feynman rules for some vertices, but I could not get the same result as given in paper, as a guideline I use ‘t Hooft’s diagrammar and the same is given in appendices of Cheng and Lee – Gauge Theory of elementary particle physics. I attach extract from one Arxiv paper, extract from diagrammar and what I was trying to write.
Could you please have a look and advise me what I do wrong?

Thank you in advance.

 

[Neitrino]

Dear all,
Could anyone pls give some feedback... May be my question senseless...
some advise pls...

 

[AlphaNumeric]

I asked a similar thing in a thread a while back.

https://www.physicsforums.com/showthread.php?t=135689

Basically you just consider the 'interaction terms' in the Lagrangian and then take the functional derivatives till you have no more fields left in that term. The remaining quantity is the Feynman rule for that vertex.

For instance, suppose you have the term $$ie\gamma^{\mu}\bar{\psi}\psi A_{\mu}$$, then taking the functional derivatives would leave you with $$ie\gamma^{\mu}$$, that's the Feynman rule. Just remember that if you've something like $$e\phi^{2}\psi$$ you'll pick up the factor of 2 from differentiating $$\phi^{2}$$ twice. I know it sounds obvious but you won't believe how often slip ups like that throw a spanner in the works!