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Evaluating Feynman diagram for coupling between scalar field and dirac particle and anti particle

  1. Oct 3, 2014 #1
    If I have a scalar field $$\alpha$$ and a Dirac particle $$\beta$$ and its anti particle $$\overline{\beta}$$ such that the three couple to give a vertex factor of $$-ik$$ when evaluating the Feynman diagram (where k is an arbitrary constant).
    How do I evaluate the first order diagram of $$\alpha \longrightarrow \beta + \overline{\beta}$$
     
  2. jcsd
  3. Oct 3, 2014 #2

    Orodruin

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    With that vertex factor, I assume you have something like ##-k \bar\beta \beta \alpha## in the Lagrangian density. It should be a simple matter of writing down the vertex factor and adding spinors for the outgoing fermions.
     
  4. Oct 3, 2014 #3
    Could you please give me an explicit expression? I'm not sure mine is correct.
     
  5. Oct 3, 2014 #4

    Orodruin

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    Since this is a homework-like question, it will be in more accordance with forum guidelines if you first show your attempt including your reasoning. I (or someone else) can then help you to iron out any misunderstandings or misconceptions.
     
  6. Oct 3, 2014 #5
    Of Course

    I believe the amplitude simply evaluates to

    $$ k\overline{U}^{(s)}V^{(s)}$$

    where U is the spinor of the Beta and V is the spinor of the anti Beta, just from simply accounting for the spinors and the vertex factor.
     
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